Prentice Hall Algebra 2

Descriptive Statistics and Histograms

For numerical data, you can find the mean, the median, and the mode.

Mean The sum of the data values in a data set divided by the number of data values
Median The middle value of a data set that has been arranged in increasing or decreasing order. If the data set has an even number of values, the median is the mean of the middle two values.
Mode The most frequently occurring value in a data set

Example 1

Find the mean, median, and mode for the following data set.

5 7 6 3 1 7 9 5 10 7
Mean fraction 5 plus 7 plus 6 plus 3 plus 1 plus 7 plus 9 plus 5 plus 10 plus 7 , over 10 end fraction . equals 6
Median 5, 7, 6, 3, 1, 7, 9, 5, 10, 7 Rearrange the numbers from least to greatest.
1, 3, 5, 5, 6, 7, 7, 7, 9, 10 The median is the mean of the two middle numbers, 6 and 7.
The median is fraction 6 plus 7 , over 2 end fraction . equals 6.5 .
Mode The most frequently occurring data value is 7.

The frequency of a data value is the number of times it occurs in a data set. A histogram is a bar graph that shows the frequency of each data value.

Example 2

Use the survey results to make a histogram for the cost of a movie ticket at various theaters.

Survey of Movie Ticket Prices
$7 $8 $7 $9 $8 $9 $8 $10 $8

A histogram of frequency by ticket price in dollars. At 7 dollars the frequency is 2, at 8 it is 4, at 9 it is 2, and at 10 it is 1. All values are approximate.

Exercises

Find the mean, the median, and the mode of each data set.

  1. negative 3 4 5 5 negative 2 7 1 8 9
  2. 0 0 1 1 2 3 3 5 3 8 7
  3. 2.4 2.4 2.3 2.3 2.4 12.0
  4. 1 1 1 1 2 2 2 3 3 4
  5. 1.2 1.3 1.4 1.5 1.6 1.7 1.8
  6. negative 4 minus 3 minus 2 minus 1 0 1 2 3 4

Make a histogram for each data set.

  1. 7 4 8 6 6 8 7 7 5 7
  2. 73 75 76 75 74 75 76 74 76 75

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Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments