Suppose that we have a sample x, y and we have calculated, and for the sample. Now an (+1)st observation becomes available. Let X-1 and be the sample mean and sample variance for the sample using all n + 1 observations.

(a) Show how

(b) Show that can be computed using and... (n 1) + (x) #+1

(c) Use the results of parts

(a) and

(b) to calculate the new sample average and standard deviation for the data of Exercise 6-30, when the new observation is x = 64.