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June 2019 p62 q6
2506
Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.
Another group of 33 people ran the same marathon. Their times (in minutes) are:
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.
Find the interquartile range of these times.
Solution
(i) Advantage: A box-and-whisker plot provides a visual summary of data distribution, showing the median, quartiles, and potential outliers, which helps in understanding the spread and shape of the data.
Disadvantage: It does not provide detailed information about individual data points or the exact distribution of data within the quartiles.
(iii)(a) To draw the box-and-whisker plot:
Identify the minimum value: 190
Identify the maximum value: 375
Calculate the median: 280
Calculate the lower quartile (LQ): 256 or 256.5
Calculate the upper quartile (UQ): 329
Draw the box from LQ to UQ with a line at the median. Extend whiskers from the minimum to LQ and from UQ to the maximum.
(iii)(b) The interquartile range (IQR) is calculated as: