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June 2011 p61 q6
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There are 5000 schools in a certain country. The cumulative frequency table shows the number of pupils in a school and the corresponding number of schools.
| Number of pupils in a school | \(\leq 100\) | \(\leq 150\) | \(\leq 200\) | \(\leq 250\) | \(\leq 350\) | \(\leq 450\) | \(\leq 600\) |
|---|---|---|---|---|---|---|---|
| Cumulative frequency | 200 | 800 | 1600 | 2100 | 4100 | 4700 | 5000 |
- Draw a cumulative frequency graph with a scale of 2 cm to 100 pupils on the horizontal axis and a scale of 2 cm to 1000 schools on the vertical axis. Use your graph to estimate the median number of pupils in a school.
- 80% of the schools have more than \(n\) pupils. Estimate the value of \(n\) correct to the nearest ten.
- Find how many schools have between 201 and 250 (inclusive) pupils.
- Calculate an estimate of the mean number of pupils per school.
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