Question 6 - A-Level Maths

Exam Board	CAIE
Module	S1 (Statistics 1)
Year	2019
Session	June
Topic	Data representation
Type	State advantages of diagram types

Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.
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. $$\begin{array} { l l l l l l l l l l l l l } 180 & 275 & 235 & 242 & 311 & 194 & 246 & 229 & 238 & 768 & 332 & 227 & 228 \end{array}$$ 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.
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
(a) On the grid below, draw a box-and-whisker plot to illustrate the times for these 33 people.
\includegraphics[max width=\textwidth, alt={}, center]{f4d040a2-6a04-49ce-98ac-8ba5c515f905-09_611_1202_1270_555}
(b) Find the interquartile range of these times.