Sample Mean and Variance From Scratch

Difficulty: Easy · Concept: Probability & Statistics — Expectation, Variance, Covariance

For a dataset $x_1, \dots, x_n$, the mean is $\bar{x} = \frac{1}{n}\sum_i x_i$, and the population variance is the average squared deviation from that mean: $\sigma^2 = \frac{1}{n}\sum_i (x_i - \bar{x})^2$. Every summary statistic on this site — standard deviation, standardization/z-scores, the Gaussian assumption behind MSE — builds on these two numbers.

Your task: implement sample_mean_and_variance(data), returning a (mean, variance) tuple. Use the population definition above (divide by $n$, not $n-1$).

Next: Standardize a Dataset (Z-Score Normalization) (a harder variant), or skip ahead to Bayes' Theorem: Posterior From Scratch