1. Copyright © 2014 Pearson Education. All rights reserved. 3.2-1 3.2 Picturing Distributions of Data LEARNING GOAL Be able to create and interpret basic bar graphs, dotplots, pie charts, histograms, stem-and-leaf plots, line charts, and time-series diagrams.

2. Copyright © 2014 Pearson Education. All rights reserved. 3.2-2 Slide 3.2- 2 Definition The distribution of a variable refers to the way its values are spread over all possible values. We can summarize a distribution in a table or show a distribution visually with a graph.

3. Copyright © 2014 Pearson Education. All rights reserved. 3.2-3 Slide 3.2- 3 Bar Graphs, Dotplots, and Pareto Charts A bar graph is one of the simplest ways to picture a distribution. Bar graphs are commonly used for qualitative data. Each bar represents the frequency (or relative frequency) of one category: the higher the frequency, the longer the bar. The bars can be either vertical or horizontal.

4. Copyright © 2014 Pearson Education. All rights reserved. 3.2-4 Slide 3.2- 4 Important Labels for Graphs (cont.) Horizontal scale and label: The categories should be clearly indicated along the horizontal axis. (Tick marks may not be necessary for qualitative data, but should be included for quantitative data.) Include a label that describes the variable shown on the horizontal axis. Legend: If multiple data sets are displayed on a single graph, include a legend or key to identify the individual data sets.

5. Copyright © 2014 Pearson Education. All rights reserved. 3.2-5 Slide 3.2- 5 Definitions A bar graph consists of bars representing frequencies (or relative frequencies) for particular categories. The bar lengths are proportional to the frequencies. A dotplot is similar to a bar graph, except each individual data value is represented with a dot. A Pareto chart is a bar graph with the bars arranged in frequency order. Pareto charts make sense only for data at the nominal level of measurement.

6. Copyright © 2014 Pearson Education. All rights reserved. 3.2-6 Slide 1.1- 6 Favorite Sports SportNumber of Students Baseball25 Basketball18 Gymnastics14 Soccer28 Tennis12 Example: Use the data below to create a bar graph.

7. Copyright © 2014 Pearson Education. All rights reserved. 3.2-7 Slide 3.2- 7 Definition A pie chart is a circle divided so that each wedge represents the relative frequency of a particular category. The wedge size is proportional to the relative frequency. The entire pie represents the total relative frequency of 100%.

8. Copyright © 2014 Pearson Education. All rights reserved. 3.2-8 Slide 1.1- 8 Blood TypeABOAB Number of donors 7594 The Red Cross Blood Donor Clinic had a very successful morning collecting blood donations. Within 3 hours, people had made donations, and the following is a table showing the blood types of the donations: Construct a pie graph to represent the data. Example:

9. Copyright © 2014 Pearson Education. All rights reserved. 3.2-9 Slide 3.2- 9 Definitions A histogram is a bar graph showing a distribution for quantitative data (at the interval or ratio level of measurement); the bars have a natural order and the bar widths have specific meaning. A stem-and-leaf plot (or stemplot) is somewhat like a histogram turned sideways, except in place of bars we see a listing of data.

10. Copyright © 2014 Pearson Education. All rights reserved. 3.2-10 Slide 3.2- 10 Line Charts Definition A line chart shows a distribution of quantitative data as a series of dots connected by lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the frequency value for the bin.

11. Copyright © 2014 Pearson Education. All rights reserved. 3.2-11 Slide 1.1- 11 Example The scores for a 12-point quiz are listed below arranged from least to greatest. 7,5,8,2,3,7,9,11,12,5,9,3,10,12,11 Using intervals of 3 points, create a histogram and line chart for the class.