Standard Deviation

Just from the mean, we don't get a sense of how spread out the numbers are.

For example, let L[i] = k(i-101) for $0 \le i \le 100$ and constant k. The mean of L is zero for any k. But, the range varies substantially.

Standard deviation is a measure of ``spread'' around the mean.

• sample variance, $\sigma^2 = \sum_{i = 0}^{n-1} (L[i]-\mu)^2 / (n-1)$,
• standard deviation = $\sqrt{\sigma^2}$.

Standard devision of above list is 58.16786 |k| (grows with range).