79. Let and denote the sample mean and variance for the sample x1, . . . ,

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79. Let and denote the sample mean and variance for the sample x1, . . . , xn and let and denote these quantities when an additional observation is added to the sample.

a. Show how can be computed from and .

b. Show that so that can be computed from , , and .

c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58 mm and a sample standard deviation of .512 mm. A 16th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard deviation for all 16 elongation observations?

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