Statistics: Informed Decisions Using Data (4th Edition)

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

Chapter 3 - Section 3.2 - Assess Your Understanding - Applying the Concepts - Page 155: 42

Answer

$MAD=544.25~dollars$ The sample standard deviation ($712$ dollars) is substantially greater then the mean absolute deviation. Maybe this difference is due to $n-1$ in the denominator of the sample standard deviation. If you change the $n-1$ by $n$ you will find $s=616.65~dollars$. It should be a good execise to compare the sample standard deviation and the mean absolute deviation for large values of $n$.

Work Step by Step

$x̅=2025.25$ (see problem 11) $MAD=\frac{Σ|x_i-x̅|}{n}=\frac{|2529-2025.25|+|1889-2025.25|+|2610-2025.25|+|1073-2025.25|}{4}=544.25$
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