Descriptive Statistics

Centre & Spread

Descriptive statistics condense raw data to reveal its shape by asking two questions: where is the centre, and how much spread is there?

The mean is sensitive to every value, while the median is robust against extremes. Always match your summary metric to the shape of your data.

Dispersion & Pitfalls

Measures of spread quantify how much values vary around the centre:

• Range: Maximum minus minimum; highly outlier-sensitive.
• Variance: $\sigma^2 = \frac{1}{n}\sum (x_i - \bar{x})^2$, the average squared deviation.
• Standard deviation: $\sigma = \sqrt{\sigma^2}$, the square root of variance, kept in the same units as the data for clear interpretation.

Common pitfall: Using the mean for skewed data. Extreme tails pull the mean away from the bulk of observations, making the median a better "typical" value. Report standard deviation, not raw variance.