Circle graphs and Venn diagrams are types of graphs that can be used to show relationships within a data set or between data sets. In this section, you will explore how to interpret and use both circle graphs and Venn diagrams.

Part 1: Circle Graphs

The Lower Colorado River Authority maintains a chain of six reservoirs, or man-made lakes, along the Colorado River. These six reservoirs are collectively called the Texas Highland Lakes and are very important sources of drinking water for people who live in Central Texas and farmers throughout the Colorado River valley. These lakes are also great places for summer fun!

The table shows the capacity, when full, of each of the six lakes in acre-feet. An acre-foot is an amount of water that will cover 1 acre of land to a depth of 1 foot. Think of it as a square prism with a base area of 1 acre and a height of 1 foot.

 Texas Highland Lakes Lake Capacity (acre-feet) Lake Buchanan 875,566 Lake LBJ 133,216 Lake Marble Falls 7,186 Lake Travis 1,134,956 Inks Lake 13,668 Lake Austin 24,644 Source: www.LCRA.org

Before making a circle graph of these data, answer the following questions.

• From the data in the table, which lake has the largest capacity? How do you know?

Interactive popup. Assistance may be required.

Lake Travis, since its capacity is the only one greater
than 1,000,000 acre-feet
• What is a reasonable estimate of the total capacity of the Texas Highland Lakes?

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What operation does the clue word “total” suggest? Interactive popup. Assistance may be required.

Since we need a reasonable estimate, we may round to the nearest thousand. The total capacity can be found by adding the capacities of the six lakes together. 876,000 + 133,000 + 7,000 + 1,135,000 + 14,000 + 25,000 = 2,190,000 acre-feet
• About what percent of the total capacity does Lake Travis, a major source of drinking water in Central Texas, hold?

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Divide the capacity of Lake Travis by the total capacity, and then convert to a percent. Because the question asks “about,” you may use an estimate with rounded values to make the arithmetic easier. Interactive popup. Assistance may be required.

Since we need a reasonable estimate, we may round to the nearest thousand.
Capacity of Lake Travis over Total Capacity Capacity of Lake Travis Total Capacity 1,135,000 over 2,190,000 1,135,000 2,190,000 ≈ 52%

The following table contains the data from the previous table in a format that will make it easy to copy and paste into the circle graph builder interactive.

 Capacity of Texas Highland Lakes 875566, Lake Buchanan 133216, Lake LBJ 7186, Lake Marble Falls 1134956, Lake Travis 13668, Inks Lake 24644, Lake Austin

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

• Copy the data from the Capacity of Texas Highland Lakes table above and paste it into the data box in the circle graph generator.
• Be sure to give the graph an appropriate title.
• Click the Plot/Update button to view your line graph.

Which two lakes hold the most capacity in the Texas Highland Lakes system?

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Which two slices of the circle graph are the largest? Interactive popup. Assistance may be required.

Lake Travis and Lake Buchanan

Which lake holds more than half of the total capacity of the Texas Highland Lakes system? How can you tell?

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Which slices of the circle graph is larger than a semicircle? Interactive popup. Assistance may be required.

Lake Travis, because its slice is larger than half of a circle.

How does the circle graph help you to see the relative size of each part of the system at a glance?

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What does each slice of the circle graph represent? Interactive popup. Assistance may be required.

The size of each slice of the circle represents the fraction (or percent) of the system that each individual lake holds. The circle graph as a whole lets you quickly see how the size of each slice compares to the sizes of the others.

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?

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What does the overlap of the two circles in a Venn diagram represent? Interactive popup. Assistance may be required.

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?

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

Practice

1. The United Kingdom is composed of England, Scotland, Northern Ireland, and Wales. The table shows the population of each of these four countries.
 Population of the United Kingdom Country Population (millions) England 52.23 Northern Ireland 1.80 Scotland 5.22 Wales 3.01

Which of the following circle graphs best displays this data?

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Look for benchmarks such as quarter circles or half circles. Interactive popup. Assistance may be required.

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

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Source of image used for this section:
• Source: w:en:User:Nv8200p, Mansfield Dam.gif, Wikimedia Commons