Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 11 Data Analysis and Statistics - Chapter Review - Page 784: 6


See below.

Work Step by Step

The mean of $n$ numbers is the sum of the numbers divided by $n$. The median of $n$ 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 mode of $n$ numbers is the number or numbers that appear(s) most frequently. Hence here the mean is: $\frac{76+ 102+ 87+ 85+ 91+ 92+ 91+ 97}{8}=90.125$. The median is the mean of the middle items in the sequence $76, 85, 87, 91, 91, 92, 97,102$, which is: $(91+91)/2=91$. The mode is $91$. The range is the difference between the largest and the smallest data value. 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 range is: $102-76=26$ and the standard deviation is: $\sqrt{\frac{(76-90.125)^2+(85-90.125)^2+...+(97-90.125)^2}{8-1}}\approx7.8274$
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