Mean, Median, and Mode

Bill Lee
billl@metnet.mt.gov

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This project is designed to teach students the meanings of the statistical vocabulary words MEAN, MEDIAN, AND MODE (MMM) through the concrete manipulation of different colored M & M's found in a single bag.

Materials
bags of M& M's (one for each student)
graph paper
colored pencils

Procedure:
Introduce students to the terms mean, median, and mode.
Mean is the same as average.
Median is the number that occurs in the middle when all the numbers are listed in numerical order.
Mode is the number that occurs the most often.

Exploration:
Give each student a bag of M & M's, a student data sheet, and a sheet of graph paper.
Have them separate the M & M's by color.

Mean:
To find the mean number by color, students should lay their graph paper in landscape position (long side horizontal, short side vertical).

Place M & M's (one in each square) in rows on graph paper, one color to each row. Students should skip a row or two between colors.

Example: (Each "X" equals one M & M)

Blue Row X X X X X

Green Row X X X X X

Orange Row X X X X X X X

Red Row X X X X X X X X

Yellow Row X X X X X X X X X X X

Brown Row X X X X X X X X X X X X X X X X X

Students can now take M & M's away from the end of the longer rows and add them to the shorter rows until all rows are the same length. (You may end up with some rows being one M & M longer than others.)

The length of a row now represents the mean. In the example above the mean would be nine. Show students how the mean can be found by traditional averaging method:
54/6=9
Have students record their mean.

Median:
Regroup the M & Ms's by color. Count each group and make a chart like the following:(order numerically least to most)

Blue 5
Green 5
Orange 7
Red 8
Yellow 11
Brown 17

The number that appears in the middle of the list is the median. In the case above two numbers share the middle, 7 and 8, so they need to averaged:
(7+8)/2=7.5 7.5 is the example median.

Have students record their median.

Mode:
Using information from the chart, make a bar graph by coloring in squares on the graph paper. Each DIFFERENT number will be represented by a bar. Color a square above each number for each time it is represtented (X stands for one square)

X
X X X X X
5 7 8 11 18

In the above example, the number 5 occurs twice so two squares are colored on the graph paper. The highest bar is the mode. (The number that occurs the most frequently.) The example mode is 5.

Have students record their mode.

Wrap up:
Students can enjoy their M & M's as you review the meanings of Mean, Median, and Mode.

Practice:
Using a chalkboard or overhead projector, guide students in finding the class M. M. & M:

Class Mean for M & Ms: Use the traditional method of averaging to find the mean for your class. (add all student means then divide by number of students)

Class Median: Organize all student medians in numerical order and find class median.

Mode: Make bar graph of all modes and determine class mode.

E-mail your class's M. M. & M by filling out the following form and sending it to host site.

From: (email address)

Teacher Name:

Class Name:

School Name:

Class Mean:

Class Median:

Class Mode:

Review:
Once all data is received, host site will transmit collective data to all sites so that students can figure out mean, median, and mode of entire group. (Can be used as test also.)