Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

In one country, there are $5000$ schools. The cumulative frequency table gives the number of pupils in a school together with the matching number of schools.
(i)[3]

Draw a cumulative frequency graph, with a scale of $2\,\text{cm}$ to $100$ pupils on the horizontal axis and a scale of $2\,\text{cm}$ to $1000$ schools on the vertical axis. Use the graph to estimate the median number of pupils in a school.

(ii)[2]

$80\%$ of the schools have more than $n$ pupils. Estimate the value of $n$, correct to the nearest ten.

(iii)[1]

Find the number of schools with between $201$ and $250$ pupils inclusive.

(iv)[4]

Calculate an estimate for the mean number of pupils per school.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Reasonable attempt at a cumulative frequency graph using upper class boundaries

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