A biology student measures the heights of six bean seedlings, in centimetres: 5, 7, 8, 12, 13 and…

Step 1. The mean. $\bar{x} = \dfrac{60}{6} = 10$ centimetres.

Step 2. The squared distances. The distances from $10$ are $-5, -3, -2, 2, 3, 5$. Their squares are $25, 9, 4, 4, 9, 25$, which add to $76$.

Step 3. The whole group. $\sigma^2 = \dfrac{76}{6} = 12.67\ \text{cm}^2$ and $\sigma = 3.56\ \text{cm}$.

Step 4. The sample. $s^2 = \dfrac{76}{5} = 15.2\ \text{cm}^2$ and $s = \sqrt{15.2} = 3.90\ \text{cm}$.