CAIE A-Level Mathematics 5.1.3 Averages and Measures of Spread

Practise calculating and interpreting the mean, median, quartiles, range and interquartile range, then comparing distributions and judging the effect of extreme values.

Exam points

calculate median and quartiles from ordered data and obtain interquartile range as Q3 minus Q1
compare two data sets using both a measure of central tendency and a measure of spread
explain how an extreme value changes the mean and range more strongly than robust measures

[Maximum number: 2]

The heights, in cm, of the 11 basketball players in each of two clubs, the Amazons and the Giants, are shown below.

Table for Question 5.1.3—Averages and spread question 1 — CAIE A-Level Mathematics AS

Find the interquartile range of the heights of the players in the Amazons.

Four new players join the Amazons. The mean height of the 15 players in the Amazons is now 191.2 cm . The heights of three of the new players are $180 \mathrm{~cm}, 185 \mathrm{~cm}$ and 190 cm .

$\mathrm{UQ}=202\text{ cm},\qquad \mathrm{LQ}=182\text{ cm}, \qquad \mathrm{IQR}=202-182=20\text{ cm}.$

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5.1.3—Averages and spread question 1