Question

Imagine a case in which we have the following two sets of exam scores : (75, 75, 75, 75) and (50, 50, 100, 100). Using this case as an example, explain why we compute measures of variability in addition to measures of central tendency.

Answer 1

mean of set 1 = (75+75+75+75)/4=75

mean of set 2 = (50+50+100+100)/4=75.

as we see that scores of two sets are different from each other but still their mean is same.

so, we also have to calculate variabity to measure the spreadness of data.

The variance measures how far each number in the set is from the mean

variance of set 1 ={(75-75)^2+(75-75)^2+(75-75)^2+(75-75)^2} / 3 = 0

this shows that there is no variability of numbers from mean.

variance of set 2 ={(50-75)^2 +(50-75)^2 +(100-75)^2 +(100-75)^2 } / 3 = 833.33

variance of set 2 shows that there is variability of numbers from their mean

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