Slide Copyright © 2009 Pearson Education, Inc. Ch. 3.1 Definition A basic frequency table has two columns: One column lists all the categories of data. The other column lists the frequency of each category, which is the number of data values in the category.

Slide Copyright © 2009 Pearson Education, Inc. The relative frequency of any category is the proportion or percentage of the data values that fall in that category: relative frequency = frequency in category total frequency Frequency The cumulative frequency of any category is the number of data values in that category and all preceding categories.

Slide Copyright © 2009 Pearson Education, Inc. EXAMPLE 3 More on the Taste Test Using the taste test data from Example 1 (page 90) create a frequency table with columns for the relative and cumulative frequencies. What percentage of the respondents gave the cola the highest rating? What percentage gave the cola one of the three lowest ratings? Solution: We find the relative frequencies by dividing the frequency in each category by the total frequency of 20. We find the cumulative frequencies by adding the frequency in each category to the sum of the frequencies in all preceding categories. Table 3.9 (on the next slide) shows the results. The relative frequency column shows that 0.10, or 10%, of the respondents gave the cola the highest rating. The cumulative frequency column shows that 14 out of 20 people, or 70%, gave the cola a rating of 3 or lower.

Slide Copyright © 2009 Pearson Education, Inc.

Slide Copyright © 2009 Pearson Education, Inc.

Slide Copyright © 2009 Pearson Education, Inc. Binning Data Definition When it is impossible or impractical to have a category for every value in a data set, we bin (or group) the data into categories (bins), each covering a range of possible data values.

Slide Copyright © 2009 Pearson Education, Inc. EXAMPLE 2 The Dow Stocks For the 30 stocks of the Dow Jones Industrial Average, Table 3.5 (p. 92) shows the annual revenue (in billions of dollars), the one-year total return, and the rank on the Fortune 500 list of largest U.S. companies. Create a frequency table for the revenue. Discuss the pros and cons of the binning choices.

Slide Copyright © 2009 Pearson Education, Inc.

Slide Copyright © 2009 Pearson Education, Inc. Teach out In Teams: Complete Questions (p. 96) : 11, 12, 13, 14 1 question per team Calculate the Relative Frequency for each data chart. Tell me something about your findings.

Slide Copyright © 2009 Pearson Education, Inc. Ch. 3.2 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.

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. Let’s create a vertical bar graph from the essay grade data in Table 3.1.

Slide Copyright © 2009 Pearson Education, Inc.

Slide Copyright © 2009 Pearson Education, Inc. Important Labels for Graphs Title/caption: The graph should have a title or caption (or both) that explains what is being shown and, if applicable, lists the source of the data. Vertical scale and label: Numbers along the vertical axis should clearly indicate the scale. The numbers should line up with the tick marks—the marks along the axis that precisely locate the numerical values. Include a label that describes the variable shown on the vertical axis.

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. A bar graph in which the bars are arranged in frequency order is often called a Pareto chart.

Slide Copyright © 2009 Pearson Education, Inc. TIME OUT TO THINK Would it make sense to make a Pareto chart for data concerning SAT scores? Explain. Thought Question – P. 102

Slide Copyright © 2009 Pearson Education, Inc. Pie Charts Pie charts are usually used to show relative frequency distributions. A circular pie represents the total relative frequency of 100%, and the sizes of the individual slices, or wedges, represent the relative frequencies of different categories. Pie charts are used almost exclusively for qualitative data. Figure 3.5 Party affiliations of registered voters in Rochester County

Slide Copyright © 2009 Pearson Education, Inc. 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%.

Slide Copyright © 2009 Pearson Education, Inc. A graph in which the bars have a natural order and the bar widths have specific meaning, is called a histogram. The bars in a histogram touch each other because there are no gaps between the categories.

Slide Copyright © 2009 Pearson Education, Inc. The stem-and-leaf plot (or stemplot) looks somewhat like a histogram turned sideways, except in place of bars we see a listing of data for each category. Figure 3.9 Stem-and-leaf plot for the energy use data from Table 3.3. Stem Leaves

Slide Copyright © 2009 Pearson Education, Inc. Another type of stem-and-leaf plot lists the individual data values. For example, the first row shows the data values 0.3 and 0.7. Figure 3.10 Stem-and-leaf plot showing numerical data—in this case, the per person carbon dioxide emissions from Table 3.11.

Slide Copyright © 2009 Pearson Education, Inc. 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.

Slide Copyright © 2009 Pearson Education, Inc. TIME OUT TO THINK Create a stem and leaf plot for the heights of people in the classroom. Make this into a histogram. Can this be made into a pie chart? Bar graph? How does the info. presented in each graphic change how it’s seen?

Slide Copyright © 2009 Pearson Education, Inc. 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. A histogram or line chart in which the horizontal axis represents time is called a time-series diagram.

Slide Copyright © 2009 Pearson Education, Inc. Figure 3.14 Time-series diagram for the homicide rate data of Table 3.14.

Slide Copyright © 2009 Pearson Education, Inc. Teach out In Teams: Complete Questions (p. 111) : 25, 26, 27, 28 1 question per team

Slide Copyright © 2009 Pearson Education, Inc. Multiple Bar Graphs and Line Charts A multiple bar graph is a simple extension of a regular bar graph: It has two or more sets of bars that allow comparison between two or more data sets. All the data sets must have the same categories so that they can be displayed on the same graph. Figure 3.18 A multiple bar graph. Source: Wall Street Journal Almanac.

Slide Copyright © 2009 Pearson Education, Inc. Figure 3.19 A multiple line chart. Source: New York Times. A multiple line chart follows the same basic idea as a multiple bar chart, but shows the related data sets with lines rather than bars.

Slide Copyright © 2009 Pearson Education, Inc. EXAMPLE 2 Graphic Conversion Figure 3.20 is a multiple bar graph of the numbers of U.S. households with computers and the number of on-line households. Redraw this graph as a multiple line chart. Briefly discuss the trends shown on the graphs. Figure 3.20 A multiple bar graph of trends in home computing. Source: Statistical Abstract of the United States.

Slide Copyright © 2009 Pearson Education, Inc. Stack Plots Another way to show two or more related data sets simultaneously is with a stack plot, which shows different data sets in a vertical stack. Although data can be stacked in both bar charts and line charts, the latter are much more common.

Slide Copyright © 2009 Pearson Education, Inc. EXAMPLE 3 Stacked Line Chart Figure 3.22 shows death rates (deaths per 100,000 people) for four diseases since Based on this graph, what was the death rate for cardiovascular disease in 1980? Discuss the general trends visible on this graph. Figure 3.22 A stack plot using stacked wedges. Sources: National Center for Health Statistics, American Cancer Society.

Slide Copyright © 2009 Pearson Education, Inc. Geographical Data The energy use data in Table 3.3 are an example of geographical data, because the raw data correspond to different geographical locations. Figure 3.23 Geographical data can be displayed with a color-coded map.

Slide Copyright © 2009 Pearson Education, Inc. Figure 3.23 Geographical data can be displayed with a color-coded map.

Slide Copyright © 2009 Pearson Education, Inc. TIME OUT TO THINK What can you learn from the histogram in Figure 3.8 that you cannot learn easily from the geographical display in Figure 3.23? (Both are reproduced on the next slide.) What can you learn from the geographical display that you cannot learn from the histogram? Do you see any surprising geographical trends in Figure 3.23? Explain.