Measures of Dispersion Topic Review summary

Key learning points

• Range = max − min; IQR = $Q_3-Q_1$ (resistant to outliers).
• Variance $\\sigma^2=\\frac{\\sum(x-\\bar x)^2}{n}$ or $\\frac{\\sum x^2}{n}-\\bar x^2$ (population form as taught).
• Standard deviation is $\\sqrt{\\text{variance}}$.
• Coding $y=\\frac{x-a}{b}$ scales SD by $|b|$.
• Compare spreads in context — units matter.

Worked example 1 — IQR

$Q_1=4$, $Q_3=11$. IQR?

Working

$Q_3-Q_1$.

Worked example 2 — SD coding

$y=2x$; effect on SD.

Working

Additive coding does not change SD.

Worked example 3 — Range = max − min; IQR = Q_3-Q_1 (resistan

Range = max − min; IQR = $Q_3-Q_1$ (resistant to outliers).

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Variance \\\\sigma^2=\\\\\\\sum(x-\\\\bar

Variance $\\\\sigma^2=\\\\frac{\\\\sum(x-\\\\bar x)^2}{n}$ or $\\\\frac{\\\\sum x^2}{n}-\\\\bar x^2$ (population form as taught).

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.