Adjust data vector to have certain variance

Question

I have a set of integers x, 0<=x<=255 I need to transform this data in that way that :

1. Average of values in set == 0
2. Variance == 1

I can meet first condition with:

array arr[];
av = average(arr);
foreach(x in arr) { x = x - av;}

But I do not know, how to meet second one.

The best idea I have: Compute current variance and divide or multiply all integers by A to get closer to desired variance. Then A=A/2 and repeat until error is small.

(Resembles basic algorithm of estimating square root of x.)

Is there another (more efficient) way of achieving this?

Answer 1

After meeting the first condition, I need to divide every number by standard deviation.