Video: Selecting Appropriate Statistical Displays

Students in Madison’s class can speak English, French, Spanish, or a collection of all three. She asks each person to list which of the three languages they speak. She wants to analyze how many people in her class speak one language and how many speak more. Which of the following would be the best choice to display the data that she collects? [A] Venn diagram [B] Line plot [C] Bar graph

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Video Transcript

Students in Madison’s class can speak English, French, Spanish, or a collection of all three. She asks each person to list which of the three languages they speak. She wants to analyze how many people in her class speak one language and how many speak more. Which of these would be the best choice to display the data that she collects? Is it A) Venn diagram, B) Line plot, or C) Bar graph?

The key bit of information in this question is that Madison is going to analyze how many people speak one language and how many speak more. Both the line plot and bar graph will show how many people speak each of the three languages. However, they will not show how many people speak more than one. This is because they will have a single total value for English, French, and Spanish. We can therefore say that a line plot and bar graph would not be the best choice to display the data.

A Venn diagram, on the other hand, can be drawn as shown. Each of the large circles or ellipses represents one of the subjects, English, French, and Spanish. The section that is shaded in pink represents those students who can speak English and French. There is also a section that represents the students that can speak French and Spanish.

We can also see a section that represents the students that speak English and Spanish. All of the students inside these three pink sections speak two of the three languages. The middle section of our Venn diagram is where all three sections overlap. This represents the students that speak English, French, and Spanish. They can speak all three languages.

Madison will then be able to analyze and compare how many people in her class speak one language, this is shaded in blue, and how many people speak more than one language. Numbers can be placed in each of the sections based on the data that Madison collects.

This example shows that 11 students speak only English. Six speak only French. And seven speak only Spanish. There are a total of 12 students who speak two languages, three plus four plus five. There are two students that speak all three languages. We can therefore conclude that the best choice would be option A, a Venn diagram.

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