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: 26


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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: $\frac{49+39+31+30+29+28+27+27+27+22+21+21}{12}=29.25$. The median is the average of the middle two in the sequence $49, 39, 31, 30, 29, 28, 27, 27, 27, 22, 21, 21$, which is: $(27+28)/2=27.5$. The median is $27$. 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: $49-21=28$ and the standard deviation is: $\sqrt{\frac{(49-29.25)^2+(39-29.25)^2+...+(21-29.25)^2}{12}}\approx7.944$
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