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SD contest This is a standard deviation contest. You must choose four numbers from the

Chapter 1, Problem 103

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QUESTION:

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.

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QUESTION:

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:

Step 1 of 3

(a)

We know that the Standard deviation measures the typical distance of the values in a distribution from the mean. So the smallest possible standard deviation for a distribution of the whole four numbers between 0 and 10 is 0. And this is possible if we choose any 4 equal whole numbers.

Let’s consider the 4 whole numbers as: 9, 9, 9, 9.

The Mean,

The Standard deviation,

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