Find the standard deviation of the numbers: (a) 3, 6, 2, 1, 7, 5; (b) 3.2, 4.6,

Question

Find the standard deviation of the numbers: (a) 3, 6, 2, 1, 7, 5; (b) 3.2, 4.6, 2.8, 5.2, 4.4; (c) 0, 0, 0, 0, 0, 1, 1, 1. (a) By adding 5 to each of the numbers in the set 3, 6, 2, 1, 7, 5, we obtain the set 8, 11, 7, 6, 12, 10. Show that the two sets have the same standard deviation but different means. How are the means related? (b) By multiplying each of the numbers 3, 6, 2, 1, 7, 5 by 2 and then adding 5, we obtain the set 11, 17, 9, 7, 19, 15. What is the relationship between the standard deviations and between the means for the two sets? (c) What properties of the mean and standard deviation are illustrated by the particular sets of numbers in (a) and (b)? Find the standard deviation of the set of numbers in the arithmetic progression 4, 10, 16, 22, ellipsis, 154.

Explanation / Answer

(1) (a)

(b)

(c)

x d = x - x-bar d^2 3 -1 1 6 2 4 2 -2 4 1 -3 9 7 3 9 5 1 1 N = 6 = 24 28 Mean, x-bar = x /N = 4 Variance, S^2 (Population) = d^2 /N = 4.67 SD, S (Population) = (Population variance) =   2.16

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