Measures of Central Tendency - Essay Example

 MEASURES OF CENTRAL TENDENCY Central tendency is a score that indicates where the centre in a distribution tends to lie. Central tendency shows the shape and nature of a given distribution. When a set of data is collected, people are usually interested in making statistical summary on the complex set of unique values for each variable that is given. The process of sampling usually refers to the describing of a distribution of various variables (Berenson, 19). Measures of central tendency are single values that describe a particular set of data by identifying the central position within the given set of data. Some books define measures of central tendency as measures of central position. When applying the use of these measures of central tendency, some measures prove to be more effective and appropriate than others (Sharpe, 10). When applying the measures of central tendency one has to know the appropriate measure to use and under what condition is it suitable to work. There are three measures of central tendency, which includes the mean, mode, and median. Mean Mean is the arithmetic average of a given set of data. Mean is the division of the sum of all available data by the number of all observations that contribute to the total sum of the data. Mean is summarizes the ratio or interval data in situations where the given set of data is symmetrical. The total frequency within each class interval concentrates at the midpoint of a given class interval (Davies, 21). To calculate the mean of a set of variables, one needs to divide the sum of all observations by the total number of the given observations. The reasons for this procedure are that the total value is dependent on two factors that are values of individual observations and the total number of observation. When determining the mean of a given set of data, one has to standardize the simple sum by evenly distributing it across all observations. The formula for calculating mean is; Mean= Total sum/total observations. Mean has several advantages as a measure of central tendency since it takes all values of the observation into account. Also, mean is unique since each set of data has its own unique mean. However, mean is susceptible to influence from other outliners. Unusual values that are numerically large or small in a given set of data can affect the outcome of mean (Davies, 22). Additionally, the mean method is not appropriate when measuring the central position of skewed data. In case of skewed data, the mean losses the ability to show the central position of the data because the skewedness always drags it from the typical value. In determining mean, some of the observation can be important than others. In such a scenario, the weighting of variables helps to attach the importance of observations to the variables. A more important observation would have greater weight than less important observations. In measures of central tendency, calculation of the geometric mean is essential. Geometric mean helps in ascertaining growth rates such as interest rates, economic growth rate and population growth rate (Sharpe, 12). Illustration; The operating budgets of Kama, John, Brenda, Fred and faith in Kansas State are 25, 30, 20, 40 and 24 dollars respectively. Find the mean. 25 +30 +20 +40 +24 =27.8 5 Median Median is the middle score in a set of particular data. When calculating the median, one has to arrange the set of data under consideration from the lowest value to the highest value. Median is an appropriate measure for ratio scale, interval, and interval data. However, this measure is inappropriate for nominal scale data since it is impossible to rank nominal data (Berenson, 2009). Median is always in the same units as the original data, and the value is always single. When calculating median of a set data, we arrange all scores in a systematic way either in descending or ascending order. When the total number of scores is an even number, the median is the average of the two mid-point values. When the total number of scores is odd numbers, the middle score becomes the median. Median is an excellent measure of central tendency since the interval between the observations is equal because an absolute zero point exists. When determining the score within an ordinal scale, there can be confusion when discreet ordinal classes are not continuous (Davies, 23). There are several advantages of median as a measure of central tendency. Firstly, median works effectively on quantitative data as well as on ordered data. Median is also unique since in every given sample only one median exists. Moreover, outliers and extreme data values do not affect the median of a set of data. Illustration 1; The following values are the number of gallons held by gas tanks 11, 10, 13, 14 19, 15, 12, 14 Find the median number of gallons. Solution: 10, 11, 12, 13,14,15,19 =13. Since the total number of the data set is an odd number, the middle number becomes the median. Illustration 2; 10, 56, 20, 78, 90, 80 Find the median of the values. Solution 10, 20, 56, 78, 80, 90 (56 + 78)/2 =67 The median is the average of the two middle numbers. Mode Mode is the value or values that occur many times in a given set of data. Mode identifies the most prevalent score in a given distribution. Mode is a simple and a crude measure of central tendency (Sharpe, 14). This measure of central tendency applies to ordinal, nominal ratio and interval scale data. Most people use the mode when dealing with nominal scale of data. This measure is not applicable when using ordered, ratio scale or interval set of data. The mode of ungrouped data is the value or values that have most appearance in that set of data. However, when data is grouped one has to first identify the modal class, and then estimate a single number mode from the modal class. In such a case, the mode is the midpoint of the modal class (Berenson, 24). Mode works well on category data; however, it has its own disadvantages .Mode may not exist meaningfully on a continuous set of data. It is also evident that the modal response may be typical since it may not lie in the centre of the ordered data. This measure of central tendency may not also be unique like mean and median. In conclusion, information from the measures of central tendency is similar since they reflect on the aspects of data values of a whole distribution. When choosing the appropriate measure of central tendency, three considerations come into play. One should first consider the either level of the concerned variable, which may be nominal, interval, ordinal or even ratio scale. In addition, one should consider the shape of the c frequencies in the distribution. Finally, one should know the usefulness of the measures of centrally tendency. Mean is mostly effective on data that is ratio or interval (Davies, 25). When ranking data and there are equal differences between the values, median becomes the most suitable measure since it is based on ranking. Therefore, median proves to be effective when the given distribution contains more than one highly untypical value. When the set distribution of data consists of nominal variable, mode is the only suitable measure to use. Mean is the most representative statistic because it not only considers the ranking of data but also considers absolute values. Mode is the best measure or central tendency compared to median and mode, therefore, becoming the most suitable measure for analysing most statistical procedures. Works Cited Sharpe, Noreen Radke, and Richard D. Veaux. Business Statistics. Boston: Addison Wesley, 2010. Print. Davies, George R., and Dale Yoder. Business Statistics, 2d Ed. New York: J. Wiley & Sons, 2011. Print. Berenson, Mark L., and David M. Levine. Basic Business Statistics: Concepts and Applications. 7th ed. Upper Saddle River, N.J.: Prentice-Hall, 2009. Print. Read More