Different types of data sets show different relationships among the data. Sometimes, you have data that appear in categories. You can use a bar graph or a Venn diagram to compare the categories of data.

Part 1: Bar Graphs

The table below shows the ten albums with the highest sales totals, in millions of albums sold, in the United States, as of 2012.

The following table contains only the title of the album and sales from the table above. The sales (in millions) are listed first, and then the title of the album.

Click the image below to open a bar graph generator in a new window. Copy the data from the Sales, Title table above, and paste it into the data box in the bar graph generator. Be sure to give the graph an appropriate title, label each axis, and then click the Graph Data button.

Need additional instructions?

• How can you tell from the bar graph which albums sold the most copies?
  
  Interactive popup. Assistance may be required.

  Check Your Answer

  The albums with the tallest bars sold the most copies.

• Use the bar graph to determine a typical number of albums sold for the 10 best-selling albums in the United States.
  Interactive popup. Assistance may be required.
  

  Need a hint?

  What is the average or median bar height? Interactive popup. Assistance may be required.
  

  Check Your Answer

  The typical number of albums sold seems to be about 16 to 17 million copies, since more bars are clustered in this range of values than in the higher numbers of copies sold.

Part 2: Venn Diagrams

A county extension agent surveyed farmers in her county to determine the number of farmers growing either rice, sesame, or both.

She learned that 35 farmers are growing rice, and 28 farmers are growing sesame. Of these farmers, 21 of them are growing both crops.

Use this information to complete the interactive below.

In the Venn diagram below, drag the appropriate number to its place in the Venn diagram. You may not use all of the number tiles. Remember that in a Venn diagram, each circle represents the total number of farmers planting that crop, and the overlapping region represents the number of farmers planting both crops.

Inside the rice circle, there are two regions. What does each region represent?

Need a hint?

What does the overlap of the two circles in a Venn diagram represent?

Check Your Answer

The region where the rice circle overlaps the sesame circle represents the farmers who are growing both rice and sesame. The regions outside the overlap represent the farmers who are growing only rice or only sesame.

In the problem, it was stated that 35 farmers are growing rice. Why does the number 35 not appear in the region of the rice circle outside the overlap?

Need a hint?

What does the overlap of the two circles in a Venn
diagram represent?

Check Your Answer

There are 35 farmers growing rice, and that number includes the 21 farmers who are growing both rice and sesame. The difference between these numbers, 35 – 21 = 14, represents the number of farmers growing only rice.

Click the image below to open a line graph generator in a new window.

• Copy the data from the Recent Best-Selling Albums: Year and Sales table above and paste it into the data box in the line graph generator.
• Be sure to give the graph an appropriate title.
• Deselect the Auto Scale check box. Use the Set Window button to manually set the graph’s viewing window with the values shown.
• Click the Plot/Update button to view your line graph.

Need additional instructions?

What patterns do you notice in the number of copies of the best-selling albums sold in the United States between 2004 and 2008?

Need a hint?

As you read the graph from left to right in this time range, does the line move upward or downward?

Check Your Answer

The number of copies of the best-selling albums each year during that time range decreased.

Use the line graph to make a general statement about how the number of copies of the best-selling album in the United States from each year since 2000 has changed.

Need a hint?

What trends do you notice in the line graph?.

Check Your Answer

The following possible answers may include:

• Overall, the number of copies of the best-selling albums each year tended to decrease since 2000, with exceptions in 2002 and 2011.
• From 2006 to 2010, the number of copies of the best-selling album each year tended to stay about the same.
• From 2008 to 2011, there was an increase in the number of copies of the best-selling album sold each year.

How does the way that a bar graph displays categorical data compare to the way that a Venn diagram displays categorical data?

Possible Answer

A bar graph shows data in categories that do not overlap, and a Venn diagram shows data in categories that may have overlapping values.

Practice

1. Match each graph with the data table that best represents the information presented in the graph.
   

   

   Check Your Answers

   Graph 1 matches Table A.
   Graph 2 matches Table B.
2. Clarice collected data in her neighborhood to show the number of front yards containing oak trees and pine trees. She learned that 25 houses had oak trees, 41 houses had pine trees, and 12 houses had both. Which number best completes the Venn diagram shown?
   
   Interactive popup. Assistance may be required.

   Need a hint?

   41 houses had pine trees, and that includes the houses with both pine trees and oak trees. Interactive popup. Assistance may be required.

   Check Your Answer

   29