You are allowed to choose four whole numbers from 1 to 10 (inclusive, without re

Question

You are allowed to choose four whole numbers from 1 to 10 (inclusive, without repeats). Which of the following is FALSE?

a.         The numbers 4, 5, 6, 7 have the smallest possible standard deviation.

b.         The numbers 1, 2, 3, 4 have the smallest possible standard deviation.

c.         The numbers 1, 5, 6, 10 have the largest possible standard deviation.

d.         The numbers 1, 2, 9, 10 have the largest possible standard deviation.

e.         The numbers 7, 8, 9, 10 have the smallest possible standard deviation.

Explanation / Answer

The correct answer is C

Explanation:

c. The numbers 1, 5, 6, 10 have the largest possible standard deviation.

n = Number of Data Values = 4

x = Sample Mean = 5.5

s2 = Sample Variance = 21.66

s = Sample Standard Deviation = 4.65

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