lesson
Area represents frequency
1 · Learn
For unequal class widths, histogram bar height is frequency density, calculated as frequency divided by class width. Bar area then represents frequency. Comparing heights alone can mislead when widths differ.
Label the vertical axis correctly. A frequency bar chart and a histogram with unequal intervals do not use the same height rule.
2 · Worked example
Class 0–10 has frequency 20, so density 2. Class 10–30 has frequency 30, so density 1.5 despite its larger frequency.
3 · Your turn
A class of width 5 has frequency 15. Find its frequency density.
Check your answer
3.
4 · Apply your learning
Draw two bars with unequal widths and verify their areas match the supplied frequencies.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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