Algebra 2 (1st Edition)

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

Chapter 11 Data Analysis and Statistics - Chapter Review - Page 784: 7

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 is: $\frac{103+ 155+ 140+ 125+ 130+ 140+ 115}{7}=129.71$. The median is the middle item in the sequence $103, 115,125, 130, 140, 140, 155$, which is: $130$ The mode is $140$. 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): $\sqrt{\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n-1}}$. Hence here the range is: $155-103=52$ and the standard deviation is: $\sqrt{\frac{(103-129.71)^2+(155-129.71)^2+...+(115-129.71)^2}{7-1}}\approx17.337$
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