## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 12 Sequences and Series - Cumulative Review - Page 848: 32

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: $\frac{54+ 58+ 49+ 60+ 63+ 58+ 42}{7}=54.857$, The median is the middle item in the sequence $42,49,54, 58, 58, 60, 63$, which is: $58$; the mode is $58$. 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: $63-42=21$, and the standard deviation is: $\sqrt{\frac{(54-54.857)^2+(58-54.857)^2+...+(42-54.857)^2}{7}}\approx6.69$

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