(a) Show that if 5x1, x2, x3, . . . , xN 6 is a data set with mean A and standard

Chapter 15, Problem 77

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QUESTION:

(a) Show that if 5x1, x2, x3, . . . , xN 6 is a data set with mean A and standard deviation s, then s1N xi - A for every data value xi. (b) Use (a) to show that every data value is bigger than or equal to A - s1N and smaller than or equal to A + s1N (i.e., for every data value x, A - s1N x A + s1N).

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QUESTION:

(a) Show that if 5x1, x2, x3, . . . , xN 6 is a data set with mean A and standard deviation s, then s1N xi - A for every data value xi. (b) Use (a) to show that every data value is bigger than or equal to A - s1N and smaller than or equal to A + s1N (i.e., for every data value x, A - s1N x A + s1N).

ANSWER:

Step 1 of 5

Suppose that  is a data set with mean  and standard deviation .

(a) Recall that the standard deviation  is given by

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