Lesson 3

The Meaning of the Mean

Est. Class Sessions: 2–3

Summarizing the Lesson

The mean and the median are both averages—they each provide a way to represent with a single number what is typical for a set of data. Often the mean and the median are about the same. Sometimes one is a better representative of what is typical than the other. Ask students to look back at their answers to Questions 13–14 and compare the means and medians they found.

Ask:

X
  • Were the means and the medians you calculated in Questions 13–14 about the same? (Yes)
  • Which average, the mean or the median, is found by “evening out” the data? (mean)
  • Which average, the mean or the median, is found by finding the middle data point? (median)

Ask students to work with a partner to answer the questions below. Students will need calculators to find the mean.

Ask:

X
  • Five students worked on a fundraiser for the school library. They collected the following amounts: $9, $10, $10, $11, and $100. Find the mean and median of the five amounts. (mean = $28, median = $10)
  • Which number represents the data better, the mean or the median? Which one value is a “typical” amount the students collected? (Since four of the amounts are close to $10 and the fifth amount is much different, the median value is more typical for this set of data.)
  • A sixth student will turn in his money late. Which value would you use to predict how much money the student will turn in? (For the reasons given above, using the median to predict an amount of $10 makes sense.)
  • Which average, the median or the mean, is affected by all of the numbers in the data set? (The mean. The 100 pulls the average up.)
  • Which average is not affected as much by big differences in the data? (The median, because it looks only at the middle number. It does not matter how large the largest—or how small the smallest—value is.)

Question 15 asks students to find the average spelling score for a set of five scores: 13, 19, 12, 20, and 11 words correct. Students must choose to use the mean or the median. The median number of words correct is 13. The mean number of words correct is 15. One advantage of using the median is that it is often easier to find. The mean score is higher in this case because the computation involves the two higher scores. Students will probably feel that a score of 15 represents the scores better than a score of 13 because it “evens out” the scores.

The Cookie Factory Assessment Master in the Teacher Guide provides additional opportunities for students to apply the strategies they have learned for finding the mean and the median of a data set.

Before students begin their work, use the Math Practices page in the Reference section of the Student Guide to discuss strategies for reading the problems so they can know the questions to answer [MPE1] and for explaining work so others can understand their thinking [MPE5].

X

Use the Cookie Factory Assessment Master to assess students' abilities to find medians and means [E5, E6] and to make predictions and generalizations using medians and means [E8].




Student Guide: 183
Answers
X
SG_Mini
+
Student Activity Book:
Master: