## Lesson: Mean, Median, and Mode Introducing the Concept

Use this lesson to introduce students to the different ways to describe data.

Materials: none

Preparation: On the chalkboard, draw and label the tally chart shown below.

Prerequisite Skills and Concepts: Students should be able to order numbers, add, subtract, and divide.

• Say: Suppose that this tally chart shows the temperatures recorded during the third week in January of this year.
Display the tally chart shown below.
• Say: Let's show this data on a line plot. On a line plot, we can use X's to show the data from the tally chart.
On the board, draw and label the line plot shown below.
• On the chalkboard, write range.
• Say: The range is the difference between the greatest number and the least number. Let's find the difference between the highest temperature and the lowest temperature in order to find the range of the temperatures that week.

Write 38 − 24 = 14 on the chalkboard.

• Say: The range is 14°.

Write mode on the board.

• Say: The mode is the number that occurs most frequently in a data set. Let's find the mode for the temperatures that week.
• Ask: Which temperature has the most X's above it on the line plot? (24°)
• Say: The mode is 24°.

On the chalkboard, write mean.

• Say: The mean is sometimes called the average. To find the mean, find the sum of the numbers in the data set and divide the sum by the number of addends. Let's add all of the temperatures in the data set and divide the sum by the number of addends.
Have a volunteer do the computation and record the mean on the board:

24 + 24 + 24 + 26 + 30 + 30 + 38 = 196
196 ÷ 7 = 28

• Say: The mean is 28°.

Write median on the board.

• Say: The median is the middle number in a data set. Let's list the temperatures in order from least to greatest and find the middle number.
Write 24 + 24 + 24 + 26 + 30 + 30 + 38 on the board.
• Ask: What is the middle number in this data set?
Students should realize that the middle number is 26.
• Say: The median is 26°.
• Ask: Could there be two middle numbers in a data set?
Some students may realize that there would be two middle numbers if there were an even number of items.
• Say: When there are two middle numbers, the mean of the two middle numbers is the median.

Write outlier on the board.

• Say: An outlier is a number that is distant from most of the other data.
• Ask: Does this data have an outlier? (yes) If it does, what is it? (38°) How does this outlier change the mean? (It makes the mean greater than the median.)
• Say: All of these terms help us describe data. Then we might analyze the data in order to make plans for the future.
• Ask: If you were planning a vacation for the third week in January of next year, why might the above data be helpful?
Lead students in a discussion about how they might use this data. They may realize that they could use this data to predict the temperatures for next year in order to determine if the third week in January would be a good time for the various vacation activities they might have in mind; it might also help them determine what type of clothing they would need to wear.