Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

The times, measured in minutes, for 13 pupils at each of two schools in a cross-country race are given in the table below. Thaters School: $38, 43, 48, 52, 54, 56, 57, 58, 58, 61, 62, 66, 75$ Whitefay Park School: $45, 47, 53, 56, 56, 61, 64, 66, 69, 73, 75, 78, 83$
(i)[4]

Draw a back-to-back stem-and-leaf diagram to show these times, with Thaters School placed on the left.

(ii)[2]

Find the interquartile range for the times recorded by pupils at Thaters School.

(iii)[2]

The times taken by pupils at Whitefay Park School are represented by $x$ minutes. Find the value of $\Sigma (x - 60)^2$.

(iv)[2]

It is stated that $\Sigma (x - 60) = 46$. Use this result, together with your answer to part (iii), to find the variance of $x$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate stem-and-leaf arrangement

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