Lecture-8-9Measures of Dispersion The measures of central tendency, such as the mean, median, and mode, do not reveal thewhole picture of the distribution of a data set. Two data sets with the same mean mayhave completely different spreads. The variation among the values of observations forone data set may be much larger or smaller than for the other data set. Consider thefollowing two data sets on the ages (in years) of all workers working for each of twosmall companies.Company 1: 47, 38, 35, 40, 36, 45, 39Company 2: 70, 33, 18, 52, 27The mean age of workers in both these companies is the same, 40 years. If we do notknow the ages of individual workers at these two companies and are told only that themean age of the workers at both companies is the same, we may deduce that the workersat these two companies have a similar age distribution. As we can observe, however, thevariation in the workers’ ages for each of these two companies is very different.Company 1 36 39 35 38 40 45 47 Company 218 27 33 52 70Thus, the mean, median, or mode by itself is usually not a sufficient measure to reveal theshape of the distribution of a data set. We also need a measure that can provide someinformation about the variation among data values. The measures that help us learn aboutthe spread of a data set are called the measures of dispersion. The measures of centraltendency and dispersion taken together give a better picture of a data set than themeasures of central tendency alone.Different Measures of Dispersion:(i)Range(ii)Variance(iii)Standard deviation and (iv)Coefficient of variation1
RangeThe range is the simplest measure of dispersion to calculate. It is obtained by taking thedifference between the largest and the smallest values in a data set. Finding the Range for Ungrouped DataRange = Largest value - Smallest valueEXAMPLE Table 1 gives the total areas in square miles of the four western South-Central states ofthe United States.