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” …