Math Background

Lesson: Mean, Median, and Mode
Developing the Concept

Use this lesson to show that double bar graphs are used to compare two sets of data.

Materials: overhead transparency

Preparation: Draw the graph shown below on an overhead transparency.

graph

Display the double bar graph to students.

  • Say: Bar graphs can be used to compare data that can be counted. Double bar graphs can be used to compare two sets of data. What are two sets of data that we can compare using this bar graph? Lead students to realize that they can compare the number of boys participating in various camp activities with the number of girls participating.
  • Ask: How many girls participate in tennis?
    Help students follow the top of the red bar for tennis to the numbers on the vertical axis. (30 girls)
  • Ask: How many boys participate in tennis?
    Help students follow the top of the blue bar for tennis to the numbers on the vertical axis. (25 boys)
  • Say: Let's compare the heights of the bars to see whether tennis is more popular with girls or with boys.
  • Ask: Which bar is higher—the red bar for girls or the blue bar for boys? Is tennis more popular with girls or with boys?
    Help students see that, since the red bar is higher, tennis is more popular with girls.
  • Ask: How many more girls than boys play tennis?
    Have a volunteer come to the board and subtract: 30 − 25 = 5. Five more girls than boys play tennis.
  • Ask: How many girls participate in swimming?
    Help students follow the top of the red bar for swimming to the numbers on the vertical axis. (35 girls)
  • Ask: How many boys participate in swimming?
    Help students follow the top of the blue bar for swimming to the numbers on the vertical axis. (35 boys)
  • Say: Let's compare the heights of the bars to see whether swimming is more popular with girls or with boys.
    Students will see that the height is the same for both bars. They should conclude that swimming is just as popular with girls as it is with boys.
  • Say: We can also use this bar graph to compare both bars together for one activity with both bars for other activities.
  • Ask: What activity is the most popular with both boys and girls? (swimming) What activity is the least popular with both boys and girls? (crafts)

    Continue to ask similar questions related to the other activities on the graph. Once students have discussed all of the data, help them make a table showing the data from the double bar graph. Have volunteers come to the board to complete the table shown below.

Participation in Camp Activities
  Tennis Swimming Canoeing Crafts
Girls 30 35 15 10
Boys 25 35 20 5
  • Direct students' attention to both the double bar graph and the table.
  • Ask: Is it easier to compare the data at a glance by using the table or by using the double bar graph?
    Students may realize that it is easier to compare data at a glance by using the double bar graph.
  • Say: Now you know that you can use a double bar graph to compare two sets of data.
  • Ask: If you were in charge of running a camp, why might a glance at this data be helpful?
    Lead students in a discussion about using the data. They may realize that they could use it to decide which activities they should be sure to offer in the future, depending on whether more girls or more boys are signed up for camp.

Wrap-Up and Assessment Hints
Encourage students to use mean, median, and mode to describe several different sets of data so they become familiar with the terms and what they mean. Assess students' understanding by having them explain to you what each term communicates about a given data set.

Houghton Mifflin Math Grade 4