Assume one collects sample of n observations {xsub1, xsub2,.......,xsubn}={xsubi}^n i=1 and based upon it, calculates the sample statistics xbarsubn, s^2subn. Suppose that new observation xsubn+1 is collected, as in engineering testing and quality control this isn't rare.
a) Determine a way to update the sample mean without recomputing the whole average, this is, compute xbar+1 in terms of xbarsubn and xbarsubn+1
B) Show that updating the sample variance is the same as computing ns^2subn+1=(n-1)s^2+ n/n+1 (xsubn+1-xsubn)^2.