A-LevelMathematicsProbability and statistics9709/51 · Oct/Nov 2022 · Q39 Marks
The Lions and the Tigers are two basketball clubs. The heights, in cm, of the 11 players in each of their first team squads are given in the table. Lions 178 186 181 187 179 190 189 190 180 169 196 Tigers 194 179 187 190 183 201 184 180 195 191 197
- (a)Draw a back-to-back stem-and-leaf diagram to represent this information, with the Lions on the left.[4]
- (b)Find the median and the interquartile range of the heights of the Lions first team squad.[3]
- (c)It is given that for the Tigers, the lower quartile is 183 cm, the median is 190 cm and the upper quartile is 195 cm. Make two comparisons between the heights of the players in the Lions first team squad and the heights of the players in the Tigers first team squad.[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 (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [B1] Correct stem can be upside down, ignore extra values (not in reverse).
- [B1] Correct Lions labelled on left, leaves in order from right to left and lined up vertically, no commas or other punctuation.
- [B1] Correct Tigers labelled on same diagram, leaves in order and lined up vertically, no commas or other punctuation. If the correct data for Lions and Tigers is transposed, treat as a single error in Lions and condone in Tigers.
- [B1] Correct single key for their diagram, need both teams identified and 'cm' stated at least once here or in leaf headings or title. SC If 2 separate diagrams drawn, SC B1 if both keys meet these criteria (Max B1, B0, B0, B1).
- [B1] Median = 186 cm
- [M1] 189 < UQ < 190 – 178 < LQ < 180
- [A1] WWW
- [B1] Comparison about central tendency in context.
- [B1] Comparison about spread in context. (Condone 'similar spread' in context.)
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