Compute the standard deviation s for n values xk stored in an array data and for the equal...

Compute the standard deviation s for n values xk stored in an array data and for the equal probabilities associated with them. The standard deviation is defined as

where the variance, V, is defined by

and the mean, , by

Write recursive and iterative versions of both V and x and compute the standard deviation using both versions of the mean and variance. Run your program for n = 500, 1,000, 1,500, and 2,000 and compare the run times.