Standard deviation

Definition

Standard deviation σ measures dispersion around the mean. A small σ means data clusters near the mean; a large σ means it is widely spread. It is the square root of the variance.

Worked example

For 4; 6; 8: x̄ = 6 and σ = √[(4 + 0 + 4)/3] ≈ 1,63.

Where it appears in the exam

Paper 2 statistics asks you to find the standard deviation with a calculator and interpret it, for example by counting the data within one standard deviation of the mean.

Step-by-step method

1. Enter the data in your calculator's statistics mode.
2. Read off the mean x̄ and the population standard deviation σ.
3. Work out x̄ − σ and x̄ + σ.
4. Interpret the spread in the context of the question.

Common mistake

Using the sample standard deviation (s) instead of the population standard deviation (σ) that CAPS uses.

Related statistics terms

• Least squares regression line
• Correlation coefficient
• Outlier

Frequently asked questions

What does standard deviation mean in Grade 12 Maths?

Standard deviation σ measures dispersion around the mean. A small σ means data clusters near the mean; a large σ means it is widely spread. It is the square root of the variance.

Which NSC paper tests standard deviation?

Standard deviation belongs to the Statistics section of CAPS Grade 12 Mathematics, which is examined in Paper 2.

How do I practise questions involving standard deviation?

Snap a question that uses standard deviation into the Snap&Learn AI solver, or work through the statistics topic guide and NSC past papers.