lesson
Separate evidence, pattern and cause
1 · Learn
A sample should represent the target population. Convenience and voluntary-response samples can be biased because some groups are easier or more motivated to include. A larger biased sample does not automatically become representative.
A time-series graph places time in order and can show trend, seasonal pattern and unusual values. It does not by itself establish the cause of a change.
A scatter graph describes association between two variables. Correlation does not prove causation. Interpolation predicts within the observed range; extrapolation goes beyond it and is usually less reliable.
2 · Worked example
Surveying only morning bus users cannot represent all travel times. A scatter trend between temperature and ice-cream sales supports association; a third factor such as season may affect both.
3 · Your turn
Explain one bias in an online voluntary survey. If data cover ages 12-16, classify a prediction at age 14 and one at age 20.
Check your answer
People choosing to respond may differ from non-responders. Age 14 is interpolation; age 20 is extrapolation and less secure.
4 · Apply your learning
Design a stratified or otherwise defensible sample for a supplied school population, then annotate a time series and scatter plot without making causal claims.
Adult guidance and safety
This is England national-curriculum core teaching, not an exam-board specification. Check prerequisite understanding, require clear working and use additional varied practice before judging fluency.
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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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