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# Describing and Displaying Categorical Data Study Guide (page 3)

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Updated on Oct 5, 2011

#### Example

Create a frequency bar chart of the orchestra members' instruments.

#### Solution

See Figure 3.5 for a bar chart illustrating the instrument frequency.

#### Example

Create a percent bar chart of the types of meals ordered for the awards banquet.

#### Solution

See Figure 3.6 for a bar chart of the percentages of meals ordered.

## Visual Displays for Categorical Data with Both Response and Explanatory Variables

Suppose a data set has a response and an explanatory variable, both of which are categorical. Pie charts and bar charts can be used to give visual displays of how the response variable might depend on the explanatory variable. For pie charts, a separate pie is created for each category of the explanatory variable.

#### Example

The instructor of the university class described in practice problem 1 was initially surprised by the results. Then she realized that whether the students used "pop," "soda," or "coke" in referring to a cola beverage probably depended on the region of the country in which the student grew up. She asked each student where he or she grew up and which term he or she used for a cola beverage. Of the students from the South, 25 used the term "coke" and four used "pop." Of the students from the Midwest, 17 used the term "pop" and 10 used "soda." Of the students from the Northeast, 21 used "soda" and six used "pop." No other region of the United States was represented in the class.

Present the data in tabular form showing both counts and relative frequencies for each response variable-explantory variable combination. Make side-by-side pie charts presenting the data.

#### Solution

The teacher has recorded the value of an explanatory variable (region) to help explain the response variable values (name used to refer to a cola beverage). It is important to notice that the relative frequencies of the response variable are computed for each region.As an illustration, the sum of the relative frequencies for the South will be one. The relative frequency of using the term "coke" for students from the South was . We do not divide by the total number in the class (83), only by the number from the South (29). See Table 3.4 and Figure 3.7 for illustrations of the data.

From the pie charts, it is easy to see that the terms used for cola beverages are quite different for various regions.Notice that these pie charts for the individual regions provide greater insight than the overall pie chart you created in practice problem 4.

In a manner similar to the pie charts, bar graphs can be used to compare the response variable for varying values of the explanatory variable. Suppose we want to graph the relative frequencies. First, form a group of bars for each category of the explanatory variable.Within each group of bars, one bar is drawn for each category of the response variable. The height of the bar depends on the relative frequency.

#### Example

Create a bar chart that shows how the term used for a cola beverage changes with region of the country.

#### Solution

See Figure 3.8 for a bar chart showing cola terminology in different regions of the country.

## Describing and Displaying Categorical Data In Short

In this lesson,we have discussed the difference in population and sample distribution. As the sample size increases, the sample distribution tends to be more like the population distribution as long as sample units are selected at random. When working with categorical variables, pie charts and bar charts give a nice visual display of the data. Sometimes, an explanatory variable helps explain differences in responses. In these cases, multiple pie charts or side-by-side bar charts can help us visualize the relationship of the explanatory variable to the response.

Find practice problems and solutions for these concepts at Describing and Displaying Categorical Data Practice Exercises.

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