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76. Let in and 3: denote the sample mean and variance — 2
for the sample x1, , x” and let xn+1 and sn+1 denote these quantities when an additional obser-
vation xml is added to the sample.
a. Show how in“ can be computed from in and xn+1v
b. Show that n 2 2 n +1(xfl+l _ifl) nSn+l = (n _1)Si+ so that 5% +1 can be computed from Jan“, in,
and 3%. 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 stande
deviation for all 16 elongation observations?

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