Question

(2.40) This is a standard deviation contest. You must choose four numbers from the whole numbers 2626 to 9595, with repeats allowed.

Choose four numbers that have the largest possible standard deviation.

(Give your answer in the form of comma separated list of numbers in ascending order.)

Answer 1

Standard deviation is a measure of how much the values in a dataset are dispersed or far away from their mean.

Formula for Standard deviation is    

So To maximize Standard deviation we need to maximize the difference of the xi  and mean() for most of the values in dataset .

So the most dispersed no. with respect to each other are 2626 and 9595 .

Finally I choose 2626, 2626, 9595 , 9595 as four nos. with maximum standard deviation because their mean is mid point of 2626 and 9595 , and all four values are very much far away from the mean 6110.5.

Final answer = 2626, 2626 , 9595 , 9595