Question

Consider a dataset with at least three values. Suppose the highest value is increased by 5 and the lowest is decreased by 5. Which of the following measure(s) would change?

		Median
		Mean
		Mean and median
		Standard deviation

Answer 1

Clearly , Median will not be affected by any change in highest and lowest values unless we change the median value .

Since we are are increasing highest value by and decreasing lowest by 5 ;overall sum will remain same as 5 and -5 will be cancelled out .As a result there will be no change in mean too.

Square deviation is squared root of sum of square of deviations of observations from mean .Since highest and lowest observation got changed ;Standard deviation will also get changed.

Hence only Standard Deviations will be changed by increasing largest observation by 5 and decreasing lowest by 5.