Section 3.1: Graphical Methods for Describing Data

Comparative Bar Charts Example 3.1: Perceived Risk of Smoking The article “Most Smokers Wish They Could Quit” noted that smokers and nonsmokers perceive the risks of smoking differently. The accompanying relative frequency table summarizes responses regarding the perceived harm of smoking for each of three groups: a sample of 241 smokers, a sample of 261 former smokers, and a sample of 502 nonsmokers.

Relative Frequency of Perceived Risk of Smoking Relative Frequency Perceived Risk SmokersFormerNonsmokers Of SmokingSmokers Very harmful Somewhat harmful Not too harmful Not harmful at all

Bar Chart

Why do we use relative frequency for bar charts? 227 boys and 251 girls in grades 4 through 6 were surveyed. Each student was asked what he or she thought was most important: getting good grades, being popular, or being good at sports. The resulting data is summarized in the following table.

Relative Frequency for Boys and Girls Boys Girls Most FrequencyRelative FrequencyRelative ImportantFrequencyFrequency Grades Popularity Sports Total

Bar Charts

Pie Charts Example: College Choice College freshman were asked if they were attending his or her first, second, or third choice of university. Fourth or higher choices were combined in a category called other. The results are summarized in a pie chart.

Pie Charts When to Use: Categorical data with a relatively small number of possible categories (Sometimes this is achieved by using an "other" category. Pie charts are most useful for illustrating proportions of the whole data set for various categories. How to Construct: 1. Draw a circle to represent the entire data set. 2. For each category, calculate the “slice” size. This is done by computing slice size = 360(category relative frequency) 3. Draw a slice of appropriate size for each category.

Example: Birds that Fish A bird is observed on how many attempts it takes to catch his prey. The bird feeds off of prey that lives in shallow water. The following table shows the frequency distribution of the bird. OutcomeFrequency Relative Frequency Prey caught on 1 st attempt Prey caught on 2 nd attempt Prey caught on 3 rd attempt 2.01 Prey not caught 94.39

Pie Chart for Birds that Fish

Segmented Bar Chart Also called stacked bar chart A graph of a frequency distribution for a categorical data set. Each category is represented by a segment of the bar, and the size of the segment is proportional to the corresponding frequency or relative frequency.

Example: Where are the men? An article gave data on gender for a community college. It was reported that 42% of students enrolled at community colleges nationwide were male and 58% were female. The following are two ways to represent this data using a segmented bar graph.

Segmented Bar Chart for Where are the Men?

Example: Sex on TV The segmented bar graph shown appeared in an article “Study: More TV shows Depicting Sexuality.” Based on this graph, it is easy to see how the proportion of television shows with sexual content differs for the different types of television shows studied.

Sex on TV Bar Chart

Try This Problem A USA Today poll of 1003 adults (August 12, 2002) asked people about their view of the current state of the U.S. economy. Based on their response, each person was put into one of five categories. Construct a pie chart using the following information.

Economic Views Unflustered – upbeat about economy Comfortable – few financial worries Anxious optimists – worried but optimistic about future Strugglers – unaffected by stock market but high anxiety about retirement Stressed and stretched – believe economy is in recession, worried about standard of living

Table for Economic Views Economic ViewRelative Frequency Unflustered.31 Comfortable.23 Anxious Optimists.10 Strugglers.16 Stressed and Stretched.20

Pie Chart

Construct a comparative bar chart A poll asked the question “All things considered, in our society today, do you think there are more advantages in being a man, more advantages in being a woman, or are there no advantages?” The responses are in the following table: ResponseWomenMen Advantage in being man Advantage in being woman No advantage Don’t Know.04.05

Comparative Bar Chart

Segmented Bar Graph Construct a segmented bar chart for the question “After school, are you home alone without adult supervision?” ResponsePercentage Never8 Some of the time15 Most of the time16 All of the time61

Segmented Bar Chart

Activity: Locating States