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 754: 19a

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: $\frac{66+68+69+71+72+72+72+ 73+ 74}{9}\approx70.778$, the median is the middle in the sequence $66,68,69,71,72,72,72, 73, 74$, which is: $72$, the mode is $72$. 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: $74-66=8$ and the standard deviation is: $\sqrt{\frac{(66-70.778)^2+(68-70.778)^2+...+(74-70.778)^2}{7}}\approx2.4394$
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