A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

6-8

DURATION
1 null

COLLECTION
Cultivating Data

# Supplemental Lesson: Measures of Central Tendency

In this "Cultivating Data" lesson, students will learn to construct data tables; calculate mean, median, mode, and range; and determine which measure of central tendency is best to use in a given circumstance.

STANDARDS

• Grades 6–8: NCTM Data Analysis and Probability

OBJECTIVE

Students will be able to:

• Define and calculate mean, median, mode, and range;
• Construct data tables that facilitate the calculation of mean, median, mode, and range; and
• Determine which measure of central tendency is best to use in a given circumstance.

TIME REQUIRED: 40 minutes, plus additional time for worksheets (may be split over two or more days)

MATERIALS

DIRECTIONS

1. Pose the following problem to your class: You have been offered a sales job at Trixie's custom bike shop. There is no salary, but you are paid a 10% commission on every bike you sell. You ask Trixie what the typical sales rep makes. She isn't sure, but she provides you with the amount of commission paid to each of the seven sales reps for the past week: \$500; \$1,000; \$50; \$11,000; \$950; \$50; \$450. Write these amounts on the board.

2. Ask the class what they think the typical sales rep makes and have them explain their thinking. Through the discussion, ensure that the following points are made:

• That week, the lowest-paid rep earned \$50 while the highest made \$11,000. This is known as the range. Indicate that range also can be shown as the difference between the greatest data value and the lowest data value. In this case, \$11,000 - \$50 = \$10,950.
• The mean commission equals the sum of the commissions divided by the number of sales reps. In this case, \$14,000/7 = \$2,000. Note that mean is sometimes called arithmetic average.
• The mode commission is the amount that appears most often (there may be more than one). In this case, \$50 is the mode because it appears twice while all the others appear only once. (One way to remember mode is that the initial letters of "most" and "often" are the first two letters of mode.)
• Demonstrate how median is determined. Line up the amounts in ascending order, i.e., \$50, \$50, \$450, \$500, \$950, \$1,000, \$11,000. Indicate that \$500, the middle amount, is the median. (One way to remember median is that the median on a highway runs down the middle.) Point out that when there is an even number of data points, calculate the mean of the two middle numbers to find the median.

3. Ask the class whether the mean (\$2,000), median (\$500), or mode (\$50) would best represent the "typical" weekly commission. Ensure that students understand that the two \$50 amounts and the one \$11,000 amount skew the mode and mean, respectively.

4. Discuss the advantages and disadvantages of each measure. Note that the mode, which is easiest to calculate, is useful in certain circumstances, for example, when a sandwich shop wants to find out its most popular sandwich, but is less useful as a measure of what is typical. The mean—which, unlike the median, doesn't require the data to be lined up in order—is subject to being skewed by unusually high or low values.

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