Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 3 - Section 3.1 - Assess Your Understanding - Applying the Concepts - Page 140: 41

Answer

$Trimmed~Mean=0.874792$ It seems that the trimmed mean is not resistant when there is a large number of observations. Read problem 47; there are many multi-millionaires and billionaires, more than 1000 in the U.S. So, if you delete one of them, it will make no difference, that is $trimmed~mean\approx mean$ and the mean is not resistant. But, if there are only a few observations, as in example 5, we can compute the trimmed mean and notice that $trimmed~mean\approx median$ and the median is resistant.

Work Step by Step

First we need to delete the values 0.79 and 0.95 from the data. $Trimmed~Mean=\frac{0.81+2×0.82+2×0.83+6×0.84+2×0.85+6×0.86+5×0.87+7×0.88+3×0.89+4×0.90+5×0.91+0.92+3×0.93+0.94}{48}=0.874792$
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