Let n and sn2 denote the sample mean and variance for the sample x1,..., xn and let n+1 and s2n+1 denote these quantities when an additional observation xn+1 is added to the sample.
a. Show how n+1 can be computed from n and xn+1.
b. Show that

so that s2n+1 can be computed from xn+1, n, and s2n.
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?

+1= (n 1)s; +- -(xn+1- x) n + 1 ns?1 n+1