Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 12 - Statistics - 12.2 Measures of Central Tendency - Exercise Set 12.2 - Page 792: 57

Answer

See below.

Work Step by Step

The midrange is the sum of the minimum and maximum data value divided by $2$. The mode of $n$ numbers is the number or numbers that appear(s) most frequently. If all items appear the same number of times, then there is no mode. The median of $n$ numbers is the middle number of the numbers when they are in order (and the mean of the middle $2$ numbers if $n$ is even). The mean of $n$ numbers is the sum of the numbers divided by $n$. a) Hence the mean: $\frac{12\cdot2+16\cdot7+16\cdot12+16\cdot17+10\cdot22+11\cdot27+4\cdot32+3\cdot37+3\cdot42+3\cdot47}{94}\approx17.27$ b) Here we have $94$ items, thus the median will be the mean of the $47$th and the $48$th item, which according to the table is: $(17+17)/2=17$ c) Hence the modes: $7,12,17$ d) Hence the midrange: $\frac{12+47}{2}=29.5$
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