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: 4

Answer

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: $\frac{35+36+36+38+41+42+45+48}{8}=40.125$. The median is the mean of the middle items in the sequence $35,36,36,38,41,42,45,48$, which is: $(38+41)/2=39.5$. The mode is $36$. 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): $\sqrt{\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}}$. Hence here the range is: $92-75=17$ and the standard deviation is: $\sqrt{\frac{(35-40.125)^2+(36-40.125)^2+...+(48-40.125)^2}{8}}\approx4.399$
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