# Special Topics in Bar Graphs

## Objectives

After completing this unit, you should be able to:

• Read and analyze double bar graphs.

## Double Bar Graphs

Double bar graphs can be found from time to time. They are used for when each data group contains two different sets of frequency data. A double bar graph is used to compare both between and within data groups. (NOTE: You can have cases where there are more than two bars per data group. We will limit our discussion here to double bar graphs. However, you can apply the same information to bar graphs with multiple bars per data group.)

Below is an example of a table that has two frequency data values per data group.

Quarterly Reports of Income and Expenses for
Dry Cleaning Associates and Co.
Quarter Income
(thousands of dollars)
Expenses
(thousands of dollars)
First Quarter

57

39
Second Quarter

107

80
Third Quarter

73

78
Fourth Quarter

118

82

Double bar graphs have many of the same attributes and advantages of regular bar graphs, however there are some major difference:

Similarities between double bar graphs and single bar graphs:

• They are relatively easy to construct, they display facts about countable data.
• They show comparisons between different data groups.

The major difference between double bar graphs and single bar graphs:

• Double bar graphs allow us to make quick generalizations about differences within data groups as well as between data groups.
• Each data group is represented by two bars.

Now let's look at the bar graph that illustrates the data presented in the table above. Note that there are two bars for each data group, and they are placed next to each other on the graph.

Quarterly Reports of Income and Expenses for
Dry Cleaning Associates and Co.

When reading double bar graphs, we often want to look at the difference in heights between the two data bars within one group. For example, the difference between the income and expenses bars for each individual quarter tells you the profit for that quarter (profit = income expenses). By paying attention, not only to individual bar heights, but differences between bar heights, you can make more generalizations from double bar graphs. Let's use the bar graph above to answer some questions.

### Example

Use the double bar graph shown above to complete the following questions.

1. Is it true that if the Dry Cleaning Associates' income is over 60 thousand dollars, then their expenses are also over 60 thousand dollars? Explain your answer.
2. In what quarters did the company experience its biggest profit and the biggest loss? Approximate both values.
3. Overall, did the Dry Cleaning Associates experience a profit or a loss for the year?

1. Is it true that if the Dry Cleaning Associates' income is over 60 thousand dollars, then their expenses are also over 60 thousand dollars? Explain your answer.
Yes, this is true. The income is over 60 thousand dollars in the 2nd, 3rd, and 4th quarters. For each of those quarters we can see that the expenses are also over 60 thousand dollars, approximately 80 thousand dollars during each quarter.

2. In what quarters did the company experience its biggest profit and the biggest loss? Approximate both values.
To answer this question we must compare the value of the income to expenses for each pair of bars, by quarter. Since the bigger the difference is between income and expenses, the larger the profit, we must observe in which quarter this difference is greatest. Visually we can determine that the greatest profit occurs in the 4th quarter. Now we must approximate this profit. Since the income is about 115 thousand and the expenses are about 80 thousand, a good estimate of the profit is 115 80 = 35 thousand dollars.
The only quarter in which the expenses were bigger than the income is the third quarter. Income expenses = profit, and income is about 70 thousand, while expenses are about 75 thousand. Therefore, 70 75 = 5. We can see that there is a negative profit level, which represents a loss of 5 thousand dollars in the third quarter.

3. Overall, did the Dry Cleaning Associates experience a profit or a loss for the year?
We can see that in three of the four quarters, income was greater than expenses. Overall, there was a profit, because the amount lost in the third quarter is not nearly as much as the amount gained in the other three quarters. The graph does not tell us precisely how much is gained or lost, but it does gives us a good estimate, as well as a strong sense of any trends that have occurred.

Now try the practice for reading and analyziing double bar graphs.