lesson
A cumulative count includes earlier classes
1 · Learn
Cumulative frequency adds frequencies up to each upper boundary. It helps estimate how many observations are below a value and locate medians or quartiles in grouped data. Estimates depend on the grouped information and graph.
Do not plot ordinary class frequencies and label them cumulative. A cumulative total should not decrease as the boundary increases.
2 · Worked example
After the second of those classes, 11 observations have been counted; the final total is 20.
3 · Your turn
Find cumulative frequencies for class frequencies 3,5,8,4.
Check your answer
3, 8, 16, 20.
4 · Apply your learning
Plot a cumulative graph at upper boundaries and label any estimated percentile as an estimate.
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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