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6
The total 18 shared over 3 observations gives 6.
Class 6 · English Medium · Cambridge · Mathematics
Data, probability and written reasoning
Interpret data and probability, then explain what a summary does and does not show.
About this lesson and its coverage
Shared cross-level core and stretch unit. Start with the core questions, then use the stretch example for deeper work. The same unit is available in related class and board pathways; it is not a full grade-specific or examination-specification course. A teacher should select the appropriate depth and further topics.
Learn the idea
The mean shares a total equally among all observations; the median is the middle ordered value. They describe different features. Probability expresses a chance between zero and one under a model. A sample can be unrepresentative, and an association alone does not establish a cause.
Worked example
For 2, 3, 3, 4, 18, the mean is 30/5 = 6, while the median is 3. The high value 18 pulls the mean above most observations. Neither number alone describes all the variation.
- Identify observations, units and how they were collected.
- Choose and calculate a suitable summary.
- Explain the result and one limitation.
Stretch example
A binomial model counts successes in a fixed number of independent trials with the same chance per trial. With five independent trials and success probability 0.4 per trial, P(X=2) = 10 × 0.4² × 0.6³ = 0.3456. This is the model’s chance of exactly two successes, about 35 in 100 comparable repetitions; dependence or changing chances would invalidate this calculation.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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4
Order as 2,3,4,7,9; the middle is 4.
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1/2
Three even outcomes among six equally likely outcomes give 3/6 = 1/2.
Write in your own words. A guardian or teacher should review this response.
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Its members may share interests that other pupils do not, so its answers need not represent the school.
Explain the selection problem in plain language.
Write in your own words. A guardian or teacher should review this response.
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No. Prior knowledge, support and other differences could influence both.
Give a plausible alternative explanation without dismissing the association.
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0.375
There are 6 such sequences out of 16 equally likely sequences.
Write in your own words. A guardian or teacher should review this response.
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If the selection systematically excludes a relevant group, adding more observations of the same kind does not fix that exclusion.
Explain the collection mechanism; size alone does not ensure representativeness.
Progress and browser storage
Notebook challenge, sources and further study
Describe a small dataset
Collect or invent ten clearly labelled observations and compare their mean and median.
Review with a guardian or teacher
- State whether the data are observed or invented.
- Explain both summaries in context.
- Give one limit to the conclusion.
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