Question 1.67

1.67A standard deviation contest.

You must choose four numbers from the whole numbers 10 to 20, with repeats allowed.

  1. Choose four numbers that have the smallest possible standard deviation.
  2. Choose four numbers that have the largest possible standard deviation.
  3. Is more than one choice possible in (a)? In (b)? Explain.

1.67

(a) Picking the same number for all four observations results in a standard deviation of 0. (b) Picking 10, 10, 20, and 20 results in the largest standard deviation. (c) For part (a), you may pick any number as long as all observations are the same. For part (b), only one choice provides the largest standard deviation.