Thinking Mathematically (6th Edition)

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

Chapter 12 - Statistics - Chapter Summary, Review, and Test - Review Exercises - Page 835: 28

Answer

$\approx24.32$

Work Step by Step

The range can be obtained by subtracting the minimum data value from the maximum data value. Hence here the range is: $86-10=76$ The mean of $n$ numbers is the sum of the numbers divided by $n$. Hence the mean: $\frac{10+30+37+40+43+44+45+69+86+86}{10}=49$ The standard deviation of $x_1,x_2,...,x_n$ is (where $\overline{x}$ is the mean of the data values): $\sqrt{\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n-1}}$. Hence here the the standard deviation is: $\sqrt{\frac{(10-49)^2+(30-49)^2+(37-49)^2+(40-49)^2+(43-49)^2+(44-49)^2+(45-49)^2+(69-49)^2+(86-49)^2+(86-49)^2}{10-1}}\approx24.32$
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