lesson
A large sample can still be biased
1 · Learn
A sample should represent the population relevant to the question. Asking only people leaving a sports club about exercise habits can exclude many other residents. Increasing that biased sample's size does not remove the selection problem.
Random selection and careful question wording can reduce bias, but non-response and measurement problems still need discussion. Describe who was actually observed before generalising.
2 · Worked example
A town survey of bus users conducted only at 8 am misses many afternoon users. A broader sampling schedule addresses a different issue from merely asking more people at 8 am.
3 · Your turn
Why is a school lunch survey answered only by members of the cooking club not automatically representative of all pupils?
Check your answer
Club membership may be related to food interests; pupils outside the club are excluded from selection.
4 · Apply your learning
Design a sampling plan with a defined population and explain one remaining limitation.
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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