Correlation from scratch

You will write your own functions for the mean, the sample standard deviation and the correlation coefficient. The checker compares them with the beans of the lesson and with the statistics module.

The idea. The sample standard deviation is $s = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n - 1}}$. The correlation coefficient is $r = \dfrac{1}{n - 1}\sum z_x z_y$, where each z-score is $(x - \bar{x})/s$.

Your tasks.

1. Finish mean(values).
2. Finish sample_sd(values). Divide by $n - 1$.
3. Finish correlation(xs, ys). Use z-scores and divide the sum of their products by $n - 1$.