Why do we need to study the variation of a collection of data? Why isn’t the ave

Question

Why do we need to study the variation of a collection of data? Why isn’t the average itself adequate? What makes the standard deviation more valuable as a measure of variation than the easier to compute range?

Consider robin’s eggs; the mean weight of a collection of robin eggs is 0.72 ounce and the standard deviation is 0.12 ounce. Now consider elephants; the men weight of elephants in the zoo is 6.42 tons, with a standard deviation of 1.07 tons. The units of measurement are different and there is a great deal of difference between the weight of an elephant and that of a robin’s egg. Yet, the coefficient of variation is about the same for both. Comment on this.

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Explanation / Answer

Average is not enough to study the things. It is necessary to go to dispersion I.e the deviation of average among the values. So in the study of dispersion, range is only an approximate measure. S.D is a suitable measure to measure variation. Regarding the example these are two different problems. There is no any relation between egg weight and elephants weight even though the c.v is same. Consider two series 2,8 and 4,6. The mean is same. But how it variegated among the values is important. So S.D is necessary.

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