1. Chapter 13 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND

2. Copyright © 2009 Pearson Education, Inc. Chapter 13 Section 3 - Slide 2 Chapter 13 Statistics

3. Chapter 13 Section 3 - Slide 3 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Frequency distributions Histograms, frequency polygons, stem-and-leaf displays

4. Copyright © 2009 Pearson Education, Inc. Chapter 13 Section 3 - Slide 4 Section 3 Frequency Distributions

5. Chapter 13 Section 3 - Slide 5 Copyright © 2009 Pearson Education, Inc. Frequency Distribution A piece of data is a single response to an experiment. A frequency distribution is a listing of observed values and the corresponding frequency of occurrence of each value.

6. Chapter 13 Section 3 - Slide 6 Copyright © 2009 Pearson Education, Inc. Example The number of pets per family is recorded for 30 families surveyed. Construct a frequency distribution of the following data: 443333 2 2 1 0 22222 21111 11111 00000

7. Chapter 13 Section 3 - Slide 7 Copyright © 2009 Pearson Education, Inc. Solution 24 43 82 101 60 FrequencyNumber of Pets 443333 2 2 1 0 22222 21111 11111 00000

8. Chapter 13 Section 3 - Slide 8 Copyright © 2009 Pearson Education, Inc. Rules for Data Grouped by Classes The classes should be of the same “width.” The classes should not overlap. Each piece of data should belong to only one class.

9. Chapter 13 Section 3 - Slide 9 Copyright © 2009 Pearson Education, Inc. Definitions Midpoint of a class is found by adding the lower and upper class limits and dividing the sum by 2.

10. Chapter 13 Section 3 - Slide 10 Copyright © 2009 Pearson Education, Inc. Example The following set of data represents the distance, in miles, that 15 randomly selected second grade students live from school. Construct a frequency distribution with the first class 0  2. 0.27.41.59.64.8 1.35.70.85.90.5 8.73.89.75.36.8

11. Chapter 13 Section 3 - Slide 11 Copyright © 2009 Pearson Education, Inc. Solution First, rearrange the data from lowest to highest. 9.79.68.7 7.46.85.9 5.75.34.8 3.81.51.3 0.80.50.2 15 3 8.4 -10.4 2 6.3 - 8.3 4 4.2 - 6.2 1 2.1 - 4.1 5 0 - 2 Frequency # of miles from school Total

12. Copyright © 2009 Pearson Education, Inc. Chapter 13 Section 3 - Slide 12 Section 4 Statistical Graphs

13. Chapter 13 Section 3 - Slide 13 Copyright © 2009 Pearson Education, Inc. Circle Graphs Circle graphs (also known as pie charts) are often used to compare parts of one or more components of the whole to the whole.

14. Chapter 13 Section 3 - Slide 14 Copyright © 2009 Pearson Education, Inc. Example According to a recent hospital survey of 200 patients, the following table indicates how often hospitals used four different kinds of painkillers. Use the information to construct a circle graph illustrating the percent each painkiller was used. 200 24Other 16Acetaminophen 104Ibuprofen 56Aspirin

15. Chapter 13 Section 3 - Slide 15 Copyright © 2009 Pearson Education, Inc. Solution Determine the measure of the corresponding central angle. 200 24 16 104 56 Number of Patients 100% Percent of Total 360  0.12  360 = 43.2  0.08  360 = 28.8  0.52  360 = 187.2  0.28  360 = 100.8  Measure of Central Angle Total Other Acetaminophen Ibuprofen Aspirin Painkiller

16. Chapter 13 Section 3 - Slide 16 Copyright © 2009 Pearson Education, Inc. Solution (continued) Use a protractor to construct a circle graph and label it properly. 8%12% Hospital Painkiller Use Aspirin 28% Ibuprofen 52% Other Acetaminophen

17. Chapter 13 Section 3 - Slide 17 Copyright © 2009 Pearson Education, Inc. Histogram A histogram is a graph with observed values on its horizontal scale and frequencies on it vertical scale. Example: Construct a histogram of the frequency distribution. 24 43 82 101 60 Frequency # of pets

18. Chapter 13 Section 3 - Slide 18 Copyright © 2009 Pearson Education, Inc. Solution 24 43 82 101 60 Frequency # of pets

19. Chapter 13 Section 3 - Slide 19 Copyright © 2009 Pearson Education, Inc. Frequency Polygon A frequency polygon is a line graph with observed values on its horizontal scale and frequencies on it vertical scale.

20. Chapter 13 Section 3 - Slide 20 Copyright © 2009 Pearson Education, Inc. Stem-and-Leaf Display A stem-and-leaf display is a tool that organizes and groups the data while allowing us to see the actual values that make up the data. The left group of digits is called the stem. The right group of digits is called the leaf.

21. Chapter 13 Section 3 - Slide 21 Copyright © 2009 Pearson Education, Inc. Example The table below indicates the number of miles 20 workers have to drive to work. Construct a stem-and-leaf display. 914352612 1621432717 41532125 12831812

22. Chapter 13 Section 3 - Slide 22 Copyright © 2009 Pearson Education, Inc. Solution Data Stem-and-Leaf 914352612 1621432717 41532125 12831812 34 53 1 1 5 6 72 2 2 2 4 5 6 7 81 3 3 4 8 90