Choose numbers with smallest and largest possible standard deviation. Is more than one choice possible in A and B?

Question

121. SD contest This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.

a. Choose four numbers that have the smallest possible standard deviation.

b. Choose Four Numbers That have the largest possible standard deviation.

c. Is More Than One Choice Possible In Either Part (a) or (b)? Explain.

 

Answer 1

(a) The smallest SD is 0, when all the numbers are the same (since repeats are allowed). There is no deviation from the mean.

(b) The largest SD is when the numbers are 0, 0, 10, 10. The mean is 5 and the variance is 4×25/4=25. The SD is 5.

(c) There are 11 possible datasets for (a), since there are 11 whole numbers between 0 and 10. For (b) there is only one dataset.