Preparation of Acetyl Salicylic Acid (Aspirin) Lab Report

Preparation of Acetyl Salicylic Acid (Aspirin) - Lab Report Example In the following experiment we embark to acquaint ourselves with a simple laboratory protocol for the synthesis of aspirin. This procedure will use acetic anhydride and sulfuric acid as the acid catalyst of the reaction. Objective: To illustrate the synthesis of the drug, aspirin and determine its purity by a chemical test Materials and methods: Synthesis of Aspirin A water- bath was prepared by filling half-way a 400mL beaker with water and the water heated to boiling point. 2.004g of salicylic acid was placed in a 125mL Erlenmeyer flask. Carefully 3mL of acetic anhydride was added to the flask and while swirling 3 drops of concentrated sulfuric acid were added. To avoid eye irritation and burns caused by acetic anhydride and sulfuric acid respectively, the chemicals were handled in the hood in gloves. The reagents were mixed and then the flask was placed in the boiling water-bath and heated for 15minutes. The setting of the practical is as shown in the diagram 1.1 below. This disso lved any solid while the solution was occasionally swirled. The Erlenmeyer flask was removed from the bath and left to cool to approximately the room temperature. The solution in the flask was then poured into a 150-mL beaker containing 20mL of ice water and mixed thoroughly before placing the beaker in an ice bath. The water destroyed any remnant of unreacted acetic anhydride and caused the insoluble aspirin to precipitate from the solution. The crystals were collected by filtering under suction with a Buchner funnel as shown in diagram 1.2 below. The side-arm of a 250mL filter flask was connected to a water aspirator with heavy wall vacuum rubber tubing. The Buchner funnel was inserted into the filter flask through a one-hole rubber stopper and a filter paper placed into the Buchner funnel making sure the paper covered all the holes. Finally the water was poured to the paper to wet it and then the water aspirator was turned on to a maximum water flow and the solution in the beaker poured into the funnel. The crystals were washed with two portions of cold water each 5mL and then followed by a one 10mL portion of cold ethanol. The suction of air was continued through the crystal for several minutes so as to dry them. The crystals were placed between several sheets of filter paper using a spatula and press-dried. A 50mL beaker was weighed before placing the crystals and reweighing the beaker. The weight and percentage yield of the crude aspirin was determined. Diagram 2: filtering using the Buchner funnel Procedure to determination of aspirin purity Three test tubes each 100 x 13 mm were labeled 1, 2, 3 and a few crystals of salicylic acid placed in the test tube-1 and in test tube-2 a small sample the newly synthesized aspirin was placed whereas for test tube-3 a small sample of crushed commercial was placed. In each of the test tubes, 5mL of distilled water was added and test tubes shaken to dissolve the crystals and a further 10 drops of 1% aqueous ferric ch loride was also added to each test tube. Observation and comparisons were made from the three test tubes and recorded. Results and Discussion Theoretical yield 2.004g salicylic acid X Weight of 50-mL beaker = 39.21 Weight of the aspirin and the beaker = 40.69 Weight of aspirin = Weight of the aspirin and the beaker - Weight of 50-mL beaker 40.69 – 39.21 = 1.48 g Weight of crude aspirin = 1.48 g Percent yield = 56.70% Chemical test with ferric chloride Presence of unreacted salicylic acid can be detected with 1% ferric chloride

US Marine Corps Combined Action Program in South Vietnam Article

US Marine Corps Combined Action Program in South Vietnam - Article Example From this paper it is clear that  the configuration of a village defense platoon is arrived upon combining a Marine squad with indigenous forces.This proved very effective in thwarting enemy forces security at the village level. CAP, which was first implemented during operations in South Vietnam, has withstood the test of time. Although there is no comprehensive statistical evidence to prove its effectiveness, first hand observations of military officers and subjective evaluations have assented to its utility. The successes met by American troops in later wars in regions such as Haiti, Bosnia, Somalia, etc, underscore CAP-style organization’s relevance and usefulness.This study outlines that  the CAP was a natural extension of the martial traditions that the US Marines excelled in. The US Marines have long understood how pacification of locals and subsequent co-option to their cause drastically improves chances of success. A robust training program for the local recruits a nd provisions for their security greatly helped with administration of localities. The validity of the CAP concept is attested by its successful implementation in war experiences in Haiti, Nicaragua, the Dominican Republic, etc during the last two centuries. CAP-style organization is especially applicable in regions where the opposition employs guerrilla warfare tactics.   In this sense, the CAP concept can be construed as counter-guerrilla warfare.... The CAP organized the hamlet defense and lived in the hamlet on a 24-hour basis. Besides hamlet security, â€Å"CAP teams provided the villagers medical care and assistance with hygiene and disease related problems. CAP teams also built simple structures and roads and conducted a variety of other civic projects aimed at helping the people. The Marine pacification program was successful in screening the people from the VC and in large part insulating them from some of the corruption and abuses of the GVN.† (Clark, 1990, p. 115) One of the early demonstrations of CAP’s organization and operation was witnessed in August of 1965 in the Vietnam theatre. The unit assembled from 3rd Battalion of 4th Marines is a case in point. Led by Lt. Col. William W. Taylor in the Phu Bai area, the unit’s Tactical Area of Responsibility (TAOR) covered half a dozen villages plus an airfield. Under pressure from enemy retaliation and realizing how thinly spread his personnel are across the terrain, the Colonel’s executive officer forwarded a plan to include members of the local militia into the 3/4 unit’s operations. After going up the ranks for evaluation and approval, the suggestion was finally assented by major General Lew Walt and Lieutenant General Victor Krulak. They foresaw how this concept could prove to be a force multiplier. It was upon their approval that General Nguyen Van Chuan of the local militia (Army of the Republic of Vietnam - ARVN) agreed to the co-operative arrangement. General Chuan gave General Walt control of local platoons in the Phu Bai jurisdiction. The results of the Phu Bai experiment encouraged further trials. The Marines instilled a combative, offensive spirit in their counterparts and gave the militia a

Measures of Central Tendency

Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is Measures of Central Tendency Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is

Physics of the Turntable :: physics sound music

Have you ever wondered how a record player works? Probably not. After all, who still listens to records? Surprisingly enough, turntables are making a come back. With the recent surge of interest in hip hop music, popular attention has been turned towards the turntable, used by DJs to provide beats, loops and scratching for virtually all of today's hip hop groups. The inner workings of the turntable may seem complex at first but after reading this paper it should become clear that, like all things, the record player works on basic principals of physics. In fact, the turntable is remarkable in that the basic physical principles behind it are quite simple. Some of these will be explored here. Please enjoy your visit. How a record player works is quite simple. A motor is somehow connected to a solid disc so that the disc is rotated at a constant speed. On top of the rotating disc (platter), The record is placed on top, with a slip mat in between. The slip mat can serve two functions. In the past to hold the record in place so that it would not rotate independently of the platter. Now, however, the slip mat serves a much different function. Instead of holding the record in place, the slip mat is now used to reduce the friction between the spinning platter and the record. This way a DJ can scratch (manually move the record, usually at high speeds) the record while the platter continues to spin underneath. Once the record is rotating, a stylus glides along the grooves and picks up the vibrations, these are then converted into audible sound. There are many different models of turntables still being manufactured. Of those being sold, it is possible to divide them into two separate categories based upon their motor system. Virtually all record players being manufactured today have either belt drive or direct drive motors. For the reasons discussed below, direct drives are accepted as the industry standard for professional DJs and turntabilists. Belt Drive - There are two advantages to the belt drive design. The motor in a belt driven turntable is set away from the platter by means of a continuous belt loop. This minimizes vibration to the platter and thus needle skipping. Also, belt drive models tend to be much cheaper than their direct drive counter parts. These advantages, however, do not balance the many short falls of the belt drive design.

Jacksonian Democrats Dbq

The election of 1828 is viewed by many as a revolution. Just as the French Revolution marked the end of aristocratic rule and the ascent of the lower classes, the election of Andrew Jackson as the seventh president of the United States likewise marked the end of the aristocratic â€Å"Virginia Dynasty† and the ascent of the common man. While Jackson was a hero of the people, having routed the British at the Battle of New Orleans and having clawed his way from poverty to wealth, he was elected primarily because his followers believed he stood for certain ideals. The Jacksonian Democrats were self-styled guardians of the United States Constitution, political democracy, individual liberty, and equality of economic opportunity. As a strict constitutional constructionist, Jackson indeed guarded what he considered the spirit of the constitution. This is borne out in his handling of South Carolina’s Nullification Crisis. By passing the â€Å"force bill,† Jackson made a statement that the position of John C. Calhoun and his home state was unconstitutional, and that he, as president, was prepared to back his ideals with force if necessary. Jackson further advanced his strict constructionist position through his handling of the â€Å"Bank War. † Nowhere in Article I, section 8 of the Constitution is the authority to create a national bank given to congress. By allowing Roger B. Taney to assist in withdrawing the federal treasury from the Bank of the U. S. and subsequently depositing the funds into regional â€Å"pet banks,† Jackson effectively disassembled what he viewed as a â€Å"monopoly of the foreign and domestic exchange† which was not â€Å"compatible with justice, with sound policy, or with the Constitution of our country. (B) Jackson’s position on the Bank of the United States also illustrates his commitment to political democracy. The Bank re-charter of 1832, though designed by Webster and Clay to embarrass Jackson publicly, backfired on the opponent Whigs. In his bank veto message of 1832, he pointed out the dangers of control of the institution by foreigners and the American mone y-elite. After all, Jackson noted, â€Å"[i]s there not danger to our liberty and independence in a bank that in its nature has so little to bind it to our country†? B) This grassroots commitment resulted in a surge in reform movements throughout the nation. The Working Men’s Party, for example, espoused the enlightenment philosophy of the Declaration of Independence in its belief that â€Å"all men are created equal. †(A) Harriet Martineau, a social observer, was indeed shocked at the absurdity of the debate â€Å"’whether the people should be encouraged to govern themselves, or whether the wise should save them from themselves. ’† Her amazement stemmed from the fact that she had observed â€Å"every man in the towns an independent citizen; every man in the country a landowner. (D) Political democracy, after all, had swept the nation. Just as his bank veto message had made apparent his support of political democracy, it also established Ja ckson as a champion of individual liberty; still, it must be made clear, that the only individuals who were beneficiaries of liberty were, in fact, white male â€Å"citizens. † The painting â€Å"The Trail of Tears† serves as a painful reminder of Jackson’s prejudiced policy of Indian Removal and the Cherokee Nation v. Georgia and Worcester v. Georgia cases. G) Ironically, Jackson’s reputation as a hero and champion of the people stems, in part, from his legendary Indian battles such as Horseshoe Bend and those with Chief Osceola and the Seminole nation. The Seneca Falls convention, while accomplishing little in the way of reform, sadly points out the inequity which existed for American women. Philip Hone, a member of the opposition party, the Whigs, points out the inequality of immigrants. He recorded in his diary â€Å"the disgraceful scene which commenced the warfare†¦. A band of Irishmen of the lowest class came out†¦armed with clubs, and commenced a savage attack upon all†¦. †(E) Perhaps the most tragic disgrace of all—the enslavement African Americans—is pointed out by the Acts and Resolutions of South Carolina. The legislature of South Carolina requested that federal laws be passed to make it illegal to print or distribute material which had the â€Å"tendency to excite the slaves of the southern states to insurrection and revolt. (F) The final ideal of which Jacksonian Democrats considered themselves champions was equality of economic opportunity. Jackson’s veto of the Bank Bill vividly illustrates this point. â€Å"It is to be regretted that the rich and powerful too often bend the acts of government to their selfish purposes. †(B) While Daniel Webster, a Whig opponent, publicly denounced Jackson’s veto as â€Å"executive pretension,†Ã‚ © Jackson firmly believed â€Å"that great evils to our country and its institutions might flow from such a concentration of power in the hands of a few men irresponsible to the people. (B) Jacksonian commitment to equality of economic opportunity is further espoused in the opinion of Jackson’s Supreme Court appointee, Chief Justice Roger B. Taney, in the Charles River Bridge v. Warren Bridge case. While Jackson’s arch-nemesis John Marshall had cleared the way for competition in Gibbons v. Ogden, Taney pointed out in characteristic Jacksonian fashion, that charters, like the Constitution, must be interpreted strictly. â€Å"There is no exclusive privilege given to them over the waters of Charles River†¦. (H) Here, surely, is commitment to equal economic opportunity. So powerful was the figure Andrew Jackson that an entire era of American history bears his name. His administration marks a fundamental paradigm shift in American ideals. Despite his opponent’s branding him a tyrant and labeling him with suc h unflattering monikers as â€Å"King Andrew,† President Jackson left an indelible mark on history as a champion of the U. S. Constitution, defender of political democracy and—to some extent—personal liberty, and equality of economic opportunity.

Its features and importance Essay

   Picture Gear Studio, DVgate Plus, Sonic Stage Other Giga Pocket PVR hardware and software with TV tuner card with remote control Support Policy One-year parts and labor warranty; 24-hour weekday toll-free support during warranty period. $19. 95 fee for phone support after 1-year warranty. Where is it available? What is its price? The SONY RS530G is available at any high end computer shop and also in the internet. Ordering this Desktop PC through the internet at eBay. com or PCExpress. com would come out cheaper than buying it here in the Philippines. Its price is $ 1850. 00 which leaves me with a total of $150. 00. The excess money I could use for extra accessories for the computer like other software’s may it be for leisure or education. III. Systems Ruled Out Obviously Workstations, Personal Digital Assistant (PDA), Mainframes, Mini-Computers and Super Computers were out of the question while choosing my preferred computer system. I don’t need a very powerful PC that is used for Computer Aided Design (CAD) nor Computer Aided Manufacturing (CAM). I don’t need a computer that would serve up to 70 users because most probably the maximum users that will be using my computer would be 3. Definitely minicomputers are out of my list for one thing they’re phased out. I don’t need a computer that would serve hundred of users at a time; I’m only a student and not a business so mainframes are crossed out of my list too. Besides mainframes are too complicated to handle as it is. Super computers on the other hand are used by businesses for task demanding extreme computing power especially in establishments for science like meteorology and finding out more on enzymes. PDA’s are too small plus it’s not practical for a student like me to buy a PDA just to set my schedule straight in school and take notes. I need a computer that would aid me in my studies just like a Micro computer. Micro computers hold floppy disk drives and CD-ROM drive or even a DVD drive that would help me in storing data need for my classes, reports and papers. It’s the most practical thing to get as of now because if I think of leaving within three years for the UK technology improves quickly and by then if ever I buy a laptop it would be phased out and it would be harder to up grade not like a desktop pc. IV. Conclusion I therefore conclude that at this time, as a student, it would be more practical for me to buy a Desktop PC that would help me in school work and at the same time entertain me for my free time. Laptops are doubled the price of a Desktop PC and is harder to upgrade unlike a Desktop PC. Usually Laptops are used by professionals who are on the go and need computers most of the time to make use of their time. References   Charles S Parker, Understanding Computers: Today & Tomorrow: 200 edition, Harcourt College Publishers www. villman. com   www. Amazon. com   www. eBay. com Note from taken from class   and gathered data from different stores :   PC Express   Stores in Greenhills Shopping Mall   Stores in Cybermall.

Corporate Crime in America essays

Corporate Crime in America essays With the latest string of corporate crime "busts," we are realizing more and more that wearing a suit and tie to work does not exempt one from criminal action. Corporate crime, though not violent in nature, is incredibly harmful with regards to society. Chief executive officers in companies such as Enron, Worldcom, and Tyco cheated their employees and investors out of millions of dollars (Puscas 2003). Much of that money was earmarked for pension benefits, retirement plans, and medical insurance for the company's workforce. Corporate crime can also be detrimental to the economy in that it reduces confidence in the stock market and other related There are two reasons why corporate crime is so prevalent (at least recently). Firstly, because those committing corporate crimes think they can get away with it, and secondly, because they believe that punishments for the crimes will be minimal. In order to fight corporate crime, we need to address these two prevailing notions. The first issue to address is criminal prosecution. It is often the case that prosecuters assigned to a case involving white collar crime will be reluctant to push the case as far as one involving drugs or violence. The reality is that corporate crime, at least in the past, was a low priority for District Attorneys. It was easier to justify sending someone to jail who had murdered another individual, then someone who falsified White collar crimes are defined as nonviolent crimes committed in commercial situations by individuals, groups, or corporations for financial gain. They include but are not limited to the following types of fraud: antitrust fraud, bankruptcy fraud, bribery, computer fraud, credit card fraud, counterfeiting, embezzlement, environmental fraud, financial fraud, government fraud, identity fraud, insider trading, insurance fraud, kickbacks, mail fraud, and trade secret ...

Jealousy lead to tragedy Essays

Jealousy lead to tragedy Essays Jealousy lead to tragedy Paper Jealousy lead to tragedy Paper A view from the bridge Arthur Miller  How does Eddies jealousy lead to tragedy?  A view from the bridge is a play that identifies the work and lives of the communities of dockworkers and longshoremen of New Yorks Brooklyn Harbor.  The author Arthur Miller has written his play focusing on the Carbone family.  Eddie Carbone is an Italian longshoreman working on the New York docks. When his wifes cousins, Marco and Rodolpho, seek refuge as illegal immigrants from Sicily, Eddie agrees to shelter them. Trouble begins when his wifes niece Catherine shows attraction towards the younger brother Rodolpho. Eddies inability to let go of Catherine, his frailty leads him to betray Rodolpho and Marco and this tragic error of judgment leads him to his death.  From the first scene Eddies frailty is shown in his obsessive need to control his niece Catherine, and his theme of appearance versus reality is more complicated because Eddie will not admit that there is a problem. To prevent other characters from knowing his motives, he hides behind what mite seem to be good reasons for his behavior. Katie, I promised your mother on her deathbed. Im responsible for you  Here you see Eddies hiding his protectiveness behind his responsibilities for Catherine and as the play progresses, we realize that deep down he wishes to keep Catherine for himself.  Eddies jealousy is dealt effectively throughout the play.  We can see from Eddies actions and the way he talks to Catherine that he has some sort of secret desire for her.  Catherine: Hi Eddie! (Eddie is pleased and therefore shy about it)  Instantly in the opening lines of the book you see Eddies true feelings for Catherine. Eddie is a grown man and has been a father figure to Catherine for many years therefore shouldnt be feeling shy when she says hi he is acting as a young man with a crush on Catherine would. Instantly his love is shown but in a very subtle, clever way. Catherine comes across flirtatious towards Eddie and he feels flattered that a young, attractive woman shows interest in him.  (Catherine enters from the bedroom with a cigar and a pack of matches)  Here! Ill light that for you! (She strikes a match and holds it to his cigar)  Catherine fusses over Eddie in a flirtatious way giving the wrong impression to Eddie.  His protectiveness over Catherine Is developed throughout the play and further on turns into jealousy.  In the first scene Eddie comes across as being protective over her as any father would be but in this case Eddie is not the father. He begins by telling Catherine that a new skirt that shes bought it too short, then tells her that shes walking wavy and he doesnt like the looks shes receiving off men he says Heads are turnin like windmills  Then follows on to tell her that he doesnt like the way she waves to men through the window. Immediately in the book you see that Eddie is a very dominant man. He sees the fact that other men are becoming interested in her and dislikes the fact she is becoming interested in them.  Catherine do me a favour, will you? Your getting to be a big girl now, you just gotta keep yourself more, you cant be so friendly kid  He begins to see that Catherine is growing up and turning into a woman. Eddie wants to protect her from growing up and is shading her from the world. But here he knows that Catherine would do anything to please him, so he asks her to do him a favor but he doesnt wait for an answer he quickly changes the subject. When both Marco and Rodolpho arrive you can instantly see Catherines interest in Rodolpho. She starts asking questions about why he hasnt married.. Eddies aware of Catherine and Rodolphos attraction towards each other and stops it before it goes further by insulting Catherine and embarrassing her in front of the visitors. Eddie uses Rodolfoà ¯Ã‚ ¿Ã‚ ½s illegal status against him and exercises his authority over him. He makes Rodolfo stop singing under the pretence that the singing is drawing attention to him and he may get discovered and picked up, to mask his feelings of jealousy and dislike towards him. (Eddie has risen, with iron control, even a smile. He moves to Catherine)  Whats the high heels for,Garbo  Eddies jealousy is growing. Catherine is showing more attention to other people than Eddie so instantly we can see that he resorts to embarrassing her in front of Rodolpho and Marco.  Eddies hatred for Rodolfo grows and he is acting on his emotions when he tells Catherine, after they have come back from the cinema that Rodolfo is only using her to get his papers so he can stay in America. Katie, hes only bowinà ¯Ã‚ ¿Ã‚ ½ to his passport  The explosion of jealousy comes when Eddie comes home drunk and finds Catherine and Rodolfo alone after having been in the bedroom together. He is so desperate; he is acting on his emotions and not thinking rationally and tells Rodolpho to leave, so Catherine agrees to go with him and Eddie tells her she isnt leaving.  Catherine: Eddie, im not gonna be a baby any more! You-  (He reaches out suddenly, draws her to him and as she strives to free herself he kisses her on the mouth) Eddie kisses Catherine to show Rodopho that Catherine is his and no one is to touch her and grips Rodolpho and also kisses him to show try and show Catherine that he isnt normaland this to Eddie was the last straw.  Eddie approaches Alfieri for help but he is unable to do anything about the marriage because she is her own person to do as she wishes.  Give me the number of the immigration bureau. Thanks. (he dials) I want to report something. Illegal immigrants. Two of them. Thats right. Four-forty-one saxon street, Brooklyn

The Importance of Providing the Best Learning Condition Through Online Public Schooling for ADD/ADHD Students

The Importance of Providing the Best Learning Condition Through Online Public Schooling for ADD/ADHD Students Albert Einstein once said, â€Å"I never teach my pupils. I only attempt to provide the conditions in which they can learn† (King p. 126). For the ADD/ADHD student, providing the best learning condition is often overwhelming and seems impossible to achieve. Online public schooling is a solution to meeting this type of student’s educational needs. An online education addresses an ADD student’s need for a more individualized, self-paced/flexible learning experience. Organizational skills are easier to manage in an online system. The community of learners, who have the same interests as the student, is broadened to include the world and not limited to a small classroom. Teachers state that â€Å"ADD students, who have difficulty learning in a traditional classroom, often do better in a setting that provides them with a more individualized, self-paced and flexible learning experience.†(Schwartz) Online public education is one way to provide this type of experience. Traditionally, in a brick and mortar school, many ADD students raise their hand to ask a question and the teacher never answers, while others get into trouble for asking too many questions. In online schooling, a student is able to think about an answer to a question before discussing it. One source has stated, â€Å"It also helps students who need time to gather their thoughts during a discussion† (Rae Jacobson). In online schools, such as Texas Connections Academy, livelessons are provided (and recorded) to aid students in these types of discussions. If the student is unable to attend the livelesson, or needs to hear the information again, the student is able to replay the lesson as many times as they need until they understand the concept. The â€Å"re-watching† of a lesson is not possible in a traditional school. An online student is able to complete the schoolwork at their own rate. Students can work at a time of the day that best fits their biological clock. â€Å"Your child can choose the time of day or night when he works best† (Rae Jacobson). Since some ADD students learn faster than others, an online school gives the student the opportunity to move on. They do not have to sit there and wait on other students to finish before moving on to the next assignment. Individualized learning and the ability to succeed, is a must for all students with learning difficulties. ADD students often have difficulty with organizational skills and completing tasks on a strict time schedule. For an ADD student, going from class to class can be challenging. A brick and mortar school requires students to carry all of their supplies and switch between teachers, assignments, and classrooms in a timely fashion (Cedar Hill High School). Traditional schools expect students to sit rigidly at a desk that does not fit the shape of the student’s body. In an online public-school system, students do not have to carry around textbooks, or supplies. A majority of their schoolwork is already organized right in front of them. Everything is at the student’s fingertips. The classroom is the students home or library. The optimum learning time for ADD students can vary. Brick and mortar high school students are on a fixed schedule and students must attend classes at a designated time and complete homework assignments in the evenings (Cedar Hill High School). Online stud ents have the ability to access and complete the class materials at any time, day or night. From my personal experience with Texas Connections Academy, I know that you are able to get access to your lessons and especially the message board, at any time of day. Your child can choose the time of day or night when he works best. â€Å"There is no set class schedule so you can attend class any time of day† (Southwestern Oklahoma State University). The burden of being super-organized and on a time crunch is virtually eliminated in an online school. Opponents of online school say â€Å"There’s something about watching a movie with a large group of people that is different from watching it all alone. Same for the classroom, it’s a group experience† While the quote itself may be true, this argument is narrow in its statement. Online education is beneficial and actually broadens the community for the ADD student. The student is no longer stuck in a small room. They have the ability to be a part of a group of people with the same interests all over the world. Thomas Jefferson believed in learning from others and practicing what he learned from others. Online schooling can increase the cultural experiences of the student. â€Å"It is important for students to have a deeper global awareness and understanding of other cultures† (Josà © Picardo) from any part of the world. The greatest way for a student to learn about another part of the world is to talk to a person who lives in that part of the world. Choos ing an online school, like Texas Connections Academy, keeps in mind the importance of social interactions and includes field trips as part of their curriculum. A student is not limited in an online classroom and has the possibility of learning more by talking to people from around the world and listening to their story of an event first hand, instead of reading a boring textbook in a traditional classroom. The impossible is possible with online schooling. Meeting an ADD/ADHD student’s individual learning style is important in order for them to have a successful educational experience that prepares them for the real world. Online schooling is the real world. The community of learners, who have the same interests as the student, is massive. Flexible learning can help meet the needs of a diverse range of students, allowing students to combine their work, their study, and even their family, and enables the students to develop skills and attributes to successfully adapt to change† (Ryerson University). Online, flexible learning, gives students the choice of when, where, and how they learn. All students can learn, if given the right condition to do so. An online education opens a door for the learning challenged student to be competitive in the 21st century. George W. Bush once said â€Å"†¦We’ll never be able to compete in the 21st century unless we have an educati on system that doesn’t quit on children, an education system that raises standards, an education that makes sure there’s excellence in every classroom† (Bush p. 2495). Online schooling is that classroom that provides excellence for ADD/ADHD students.

Analysis of Effectiveness of Behavior Patterns - Part 4 Essay

Analysis of Effectiveness of Behavior Patterns - Part 4 - Essay Example Older employees face biases and they constantly fear the job loss. The reason for this is that they are the victims of downsizing and management thinks that they are no more of any use to the organization. It is not a sensitive approach, because they have an experience and in the field of education, experienced teachers are considered to be more capable than the new teachers. Favoritism was observed in the workplace and the favorite staff members of the management enjoy extra leisure time than the other people. This evokes a sense of rejection and disappointment in other staff members. Asian and Africans also face biases in the workplace, and sometimes feel lonely and confused. They are not given the same status in the organization as the other employees. They face alienation from the staff members and usually sit by their own during the work time. There are many cues, which encourage learning and the management should adopt them in order to develop a learning environment in the organization. The first thing, which encourages employee to learn, is that manager himself is practicing, what he is asking them to do. This helps a lot and employees carry on the practice happily. Unfortunately, it is not practiced in this organization. The second thing, which encourages learning, is that regular training session should be arranged. This keeps the employees in the practice of learning and they learn new things and methodologies1. The use of technology must be encouraged and should be made compulsory. They should be introduced with the websites, containing material about their job and like this they will learn new techniques and will be aware of the new searches in their respected fields. The training session should include not only the employees of the organization but also the employees of the partner organizations can be included. T his will bring excitement in the employees and they will show more enthusiasm and interest. Different

How did the Internet has brought people to think and see the world Research Paper

How did the Internet has brought people to think and see the world globally - Research Paper Example Mass media – this is written, spoken or broadcast communication with reach to a great range of audience (Zlatar 1). This includes radio, television (TV), advertisements, billboards, movies, magazines, mobile phones, newspapers, the Internet, and so forth. As earlier noted, media acts as a highway or rather a vehicle over which there is viral transmission of content, allowing a given user to initiate communications with multiple people across the globe, with an opportunity given to each that allows them to even further spread the information to different people and places around the world (Besley and Burgess 631). A clever and dedicated person possessing a quality message can turn the whole world into a personal marketing force with the use of the mass media. In addition, Zlatar reveals that media helps people be noticeable as it helps them engage with their audience as well as allow easy location or identification of the right audience to add on the cheap costs of advertizing it presents to its users (3). Political. The mass media can be an effective tool for enabling a country’s citizens monitor the activities of their governments and use this type of information to carry out their voting decisions. The deliverable of this is a government that is more accountable for its citizens as well as responsive to the needs of the citizens. In democratic governments, Besley and Burgess assert that free media aims at scrutinizing those in power and providing the public with unbiased and accurate information so that they can appropriately act on it (632). Thus, it acts as an effectual check on the power of the government as well as the influence it has over its citizens (Etling, Faris and Palfrey 37). The past few decades have been accompanied by an unprecedented increase in mass media plus reducing costs of TV, radio, and Internet services. Besley and Burgess believes that this trend has helped bring the political activities of the world to a much larger au dience as well as help various political elements or rather organizations reach a wider range of people quickly and effectively (634). Etling, Faris and Palfrey believe that the major issue with media is the inability to take a neutral stand where some take one side of the political continuum providing them with the best biased coverage at its best and at its worst acting like a virtual propaganda machines for a given political organization and or entity (41). Media coverage occurs via a wide range of gadgets ranging from mobile phones to computers working online. Today’s politics is taking a different dimension as many are adopting media or rather the mass media to pass over their political intents as well as organize political meetings and or rallies. In addition, the prevailing generation of young people is heavily immersed into the social media, for instance, Facebook and Twitter. A number of politicians have gone further to use the short message service (SMS) to communic ate their political ideas and or information to various target audiences (Etling, Faris and Palfrey 42). Social. Today, the internet has become a basic need to almost everyone and its use has continually increased with the increasing innovation of social networks (Gladwell 42). Communication in today’s societies is propelled by the constant development of new and quality social networking sites yet some find less enthusiasm in the type of interactions that these social