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 - Quiz for Lessons 11.1.11.2 - Page 755: 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: $\frac{67+68+70+ 71+73+ 73+ 73+ 74}{8}=71.125$, the median is the mean of the middle items in the sequence $67,68, 70, 71,73, 73, 73, 74 $, which is: $(71+73)/2=72$, the mode is $73$. 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: $74-67=7$ and the standard deviation is: $\sqrt{\frac{(67-71.125)^2+(68-71.125)^2+...+(74-71.125)^2}{8}}\approx2.4206$
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