The heights, in cm, of the 11 players in each of two teams, the Aces and the Jets, are shown in the following table. Aces | 180 | 174 | 169 | 182 | 181 | 166 | 173 | 182 | 168 | 171 | 164 Jets | 175 | 174 | 188 | 168 | 166 | 174 | 181 | 181 | 170 | 188 | 190
- (a)Draw a back-to-back stem-and-leaf diagram to represent this information with the Aces on the left-hand side of the diagram.[4]
- (b)Find the median and the interquartile range of the heights of the players in the Aces.[3]
- (c)Give one comment comparing the spread of the heights of the Aces with the spread of the heights of the Jets.[1]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [B1] Correct stem, ignore extra values (not in reverse, not split).
- [B1] Correct Aces labelled on left, leaves in order from right to left and lined up vertically, no commas or other punctuation.
- [B1] Correct Jets labelled on same diagram, leaves in order and lined up vertically, no commas or other punctuation.
- [B1] Correct key for their diagram, need both teams labelled and 'cm' stated at least once here, or in leaf headings or title.
- [B1] Median = 173 [cm]. Accept Q2; must be identified.
- [M1] 180 < UQ ≤ 182 – 166 < LQ < 169. Implied if both quartile values are stated and an appropriate IQR calculated accurately.
- [A1] 13 [cm]. www. If M0 scored SC B1 for 13 www.
- [B1] Comment about spread in context, must include height. Comparison of values does not score until a comment in context is made. If values for range or IQR are stated, they must be correct or FT from 4(b). If more than one comment about spread, mark the final comment. Additional comments about central tendency score B0.
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