A-LevelMathematicsProbability and statistics9709/62 · May/June 2019 · Q610 Marks

Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.

(i)Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.[2]
(ii)The times in minutes taken to run a marathon were recorded for a group of 13 marathon runners and were found to be as follows. 180 275 235 242 311 194 246 229 238 768 332 227 228 State which of the mean, mode or median is most suitable as a measure of central tendency for these times. Explain why the other measures are less suitable.[3]
(iii)(a)Another group of 33 people ran the same marathon and their times in minutes were as follows. 190 203 215 246 249 253 255 254 258 260 261 263 267 269 274 276 280 288 283 287 294 300 307 318 327 331 336 345 351 353 360 368 375 On the grid below, draw a box-and-whisker plot to illustrate the times for these 33 people.[4]
(iii)(b)Find the interquartile range of these times.[1]

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] Advantage: comment referring to spread or range or shape
[B1] Disadvantage: comment referring to limited data information provided
[B1] Comment which identifies 768 (or ‘a very large number’) as the problem. Condone the use of 'outlier' (for part (ii))
[B1] Comment which indicates that no mode exists (e.g. all the data is different, there is no repeated number, all the values are different) (for part (ii))
[B1] Median identified as choice, dependent upon statements for mean and mode being given, even if incorrect or very general. (for part (ii))
[B1] Median, UQ and LQ values seen, may not be identified or identified correctly. (Not read from box plot unless value stated) (for part (iii)(a))
[B1 FT] Median and quartiles plotted in box on graph, linear scale (for part (iii)(a))
[B1] Correct end points, whiskers from ends of box but not through box, not at top or bottom of box (for part (iii)(a))
[B1] Uniform scale from 190 to 375 (need at least 3 linear identified points min) and labelled 'time' and 'minutes' (can be in title) (for part (iii)(a))
[B1 FT] IQR = their 329 – their 256 = 73 or 72.5 (for part (iii)(b))

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