Algebra 2 (1st Edition)

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

Chapter 11 Data Analysis and Statistics - 11.2 Apply Transformations to Data - 11.2 Exercises - Problem Solving - Page 753: 18a

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: $\frac{48+45+42.5+39+38+36.5+29+28.5+28.5}{9}\approx37.22$, the median is the middle in the sequence $48, 45, 42.5, 39, 38, 36.5,29, 28.5, 28.5$, which is: $38$, the mode is $28.5$. 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: $48-28.5=19.5$ and the standard deviation is: $\sqrt{\frac{(48-37.22)^2+(45-37.22)^2+...+(28.5-37.22)^2}{9}}\approx6.90053$
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