A-LevelMathematicsProbability and statistics9709/63 · May/June 2019 · Q710 Marks

The times in minutes taken by 13 pupils at each of two schools in a cross-country race are recorded 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)Draw a back-to-back stem-and-leaf diagram to illustrate these times with Thaters School on the left.[4]
(ii)Find the interquartile range of the times for pupils at Thaters School.[2]
(iii)The times taken by pupils at Whitefay Park School are denoted by x minutes. Find the value of ∑(x – 60)².[2]
(iv)It is given that ∑(x – 60) = 46. Use this result, together with your answer to part (iii), to find the variance of x.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] Correct stem can be upside down, ignore extra values,
[B1] Correct Thaters School labelled on left, leaves in order from right to left and lined up vertically, no commas
[B1] Correct Whitefay Park School labelled on same diagram on right hand side in order from left to right and lined up vertically, no commas
[B1] FT Correct key for their diagram, need both teams identified and 'minutes' stated at least once here or in leaf headings or title.
[SC B1] If 2 separate diagrams drawn, SCB1 if both keys meet these criteria
[B1] Both quartiles correct
[B1] FT 61 < UQ ≤ 62 – 48 < LQ < 52
[M1] Summing squares with at least 5 correct unsimplified terms
[A1] Exact value
[M1] Using two coded values in correct formula (variance or sd)
[A1] Correct answer
[SC B1] if correct variance obtained by another method give SCB1

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.