lesson
Compare centre and spread together
1 · Learn
Two groups can have the same mean but different variation. The median describes a central ordered value; range describes the distance between extremes and is sensitive to unusual values. Choose summaries suited to the question and data.
Use comparable units and consider sample size and selection. A numerical difference in a small sample is not by itself a universal claim about the wider populations.
2 · Worked example
Group A is more tightly clustered in this supplied dataset, even though both means equal 5.
3 · Your turn
For A = 4,5,6 and B = 1,5,9, compare the medians and ranges.
Check your answer
Both medians are 5. A has range 2 and B range 8.
4 · Apply your learning
Construct two five-value datasets with the same median but different ranges and explain what the summaries hide.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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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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