79. Let and denote the sample mean and variance for the sample 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?