A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2018 · Q711 Marks

The heights, in cm, of the 11 members of the Anvils athletics team and the 11 members of the Brecons swimming team are shown below. Anvils 173 158 180 196 175 165 170 169 181 184 172 Brecons 166 170 171 172 172 178 181 182 183 183 192

(i)Draw a back-to-back stem-and-leaf diagram to represent this information, with Anvils on the left-hand side of the diagram and Brecons on the right-hand side.[4]
(ii)Find the median and the interquartile range for the heights of the Anvils.[3]
(iii)The heights of the 11 members of the Anvils are denoted by x cm. It is given that Σx = 1923 and Σx² = 337 221. The Anvils are joined by 3 new members whose heights are 166cm, 172cm and 182 cm. Find the standard deviation of the heights of all 14 members of the Anvils.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] Correct stem, up or down
[B1] Correct Anvils labelled on left, leaves in order from right to left and lined up vertically, no commas
[B1] Correct Brecons labelled on same diagram on right hand side in order from left to right and lined up vertically, no commas
[B1] Correct key, not split, both teams, at least one with cm
[B1] Correct median (or Q2)
[M1] Either UQ = 181 ± 4, or LQ = 169 ± 4 and evaluating UQ – LQ
[A1] Correct answer from 181 and 169 only (IQR = 12)
[M1] Correct unsimplified expression for Σx and Σx², may be implied
[M1] Correct unsimplified mean
[M1] Correct unsimplified variance using 14, their Σx and their Σx², not using 1923 and/or 337221
[A1] Correct answer (S d = 9.19)

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