Suppose that we have a sample x1, x2, . . ., xn and we have calculated xn and sn2 for the sample. Now an (n + 1)st observation becomes available. Let xn + 1 and sn2 + 1 be the sample mean and sample variance for the sample using all n + 1 observations.
(a) Show how xn + 1 can be computed using xn and xn + 1.
(b) Show that

(c) Use the results of parts (a) and (b) to calculate the new sample average and standard deviation for the data of Exercise 6-22, when the new observation is x38 =64.

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n+ 1