Algebra 2 (1st Edition)

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

Chapter 11 Data Analysis and Statistics - 11.1 Find Measures of Central Tendency and Dispersion - 11.1 Exercises - Problem Solving - Page 748: 28


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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: $\frac{97+102+106+110+111+113+114+114+116+120}{10}=110.3$. The median is the average of the middle two in the sequence $ 97, 102, 106,110, 111, 113, 114, 114, 116, 120$, which is: $(111+113)/2=112$. The mode is $114$. 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: $120-97=23$, and the standard deviation is: $\sqrt{\frac{(97-110.3)^2+(102-110.3)^2+...+(120-110.3)^2}{10}}\approx6.881$
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