A-LevelMathematicsProbability and statistics9709/52 · May/June 2021 · Q710 Marks

The heights, in cm, of the 11 basketball players in each of two clubs, the Amazons and the Giants, are shown below. Amazons 205 198 181 182 190 215 201 178 202 196 184 Giants 175 182 184 187 189 192 193 195 195 195 204

(a)State an advantage of using a stem-and-leaf diagram compared to a box-and-whisker plot to illustrate this information.[1]
(b)Represent the data by drawing a back-to-back stem-and-leaf diagram with Amazons on the left-hand side of the diagram.[4]
(c)Find the interquartile range of the heights of the players in the Amazons.[2]
(d)Four new players join the Amazons. The mean height of the 15 players in the Amazons is now 191.2 cm. The heights of three of the new players are 180 cm, 185 cm and 190 cm. Find the height of the fourth new player.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

B1 Reference to either including all/raw data or further statistical processes are possible that cannot be found using data from box-and-whisker, eg frequency, mean, mode or standard deviation not only median, IQR, range or spread which can be found from both.
B1 Correct stem can be upside down, ignore extra values
B1 Correct Amazons labelled on left, leaves in order from right to left and lined up vertically (less than halfway to next column), no commas or other punctuation.
B1 Correct Giants labelled on same diagram, leaves in order and lined up vertically (less than halfway to next column), no commas or other punctuation.
B1 Correct single key for their diagram, need both teams identified and 'cm' stated at least once here or in leaf headings or title.
M1 201 < UQ < 205 – 181 < LQ < 184
A1 WWW
B1 Both Σ₁₁ and Σ₁₅ found. Accept unevaluated.
M1 Forming an equation for the height using their Σ₁₁ and Σ₁₅.
A1

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