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Find the Mean,
Median, and Range
(A Mathematical Game)

Subjects

• Mathematics
  -- Statistics

Grades

• 3-5
• 6-8
• 9-12

Brief Description

This activity reviews mean, median, and range (MMR).

Objectives

Students will

• demonstrate an understanding of the concepts of mean, median, and range.

Keywords

measurement, statistics, data, average, mean, median, sum, order, difference, decimal, fraction, numerator, denominator, quotient, divisor, dividend, repeating decimal, terminating decimal

Materials Needed

• a deck of playing cards for each pair (or group of four) students
• paper and pencils
• calculator (optional)

The Lesson

Before playing this game, review with students how to find the mean, median, and range of a collection of numbers (data).

Distribute a deck of cards to each pair of students. Have students shuffle the cards and deal 5 cards to each participant.

Once the cards are dealt, students will spread their cards face up and arrange them from least to greatest. They will figure the mean, median, and the range for their set of cards and write those numbers on a sheet of paper. (Scroll down to see a sample chart.)

The mean is the average of all cards: add the number/value of each card and divide by the number of cards.

The median is the value on the face of the card in the middle of all the cards when the cards are spread from lowest to highest.

The range is the difference between the card with the lowest value and the card with the highest value. For example, if the lowest card in a student's group of cards is a 3 and the highest is a 9, the range is 6. (9 - 3 = 6)

Each student will calculate the mean, median, and range for her/himself and partner. Once they have their data (MMR), they will each add the mean, median, and range to get a "total" point value of the set of cards (data) played in that round. They will check each other's math.

For example: if Student A's mean is 5-4/5, median is 5, and range is 6, then 5-4/5 + 5 + 6 = 16-4/5 points for that round of play. The students' chart might look something like this…

Each team continues to play and record their scores until they run out of cards. Each time cards are dealt is considered another set. NOTES:

• The reason for all students to track the scores of all others in the pair/group is to build accountability.
• You might allow students to use a calculator to check their calculations for accuracy, but the initial calculations should be done without a calculator.

• The dealer might vary the number of cards that are dealt at each round of play. That will ensure that the students practice finding the median with an odd number of data and an even number. (When there is an even number of cards, then the two middle cards are averaged to find the median.) An even number of data requires averaging the two numbers in the middle of the data.)
• Include face cards or delete them from the deck. The easiest way to include them (for younger students) is to let the ace represent a value of 1 and for all face cards to represent the value of 10. With older students, you can vary that by allowing students to use the ace to represent a 1 or an 11 -- their choice. You can also allow the face cards to represent different values, for example, the Jack could have a value of 10, the Queen a value of 11, and the King a value of 12.
• When figuring the mean, present it as a decimal instead of a fraction.
• Another variation might be to have students play in groups of four instead of in pairs.

Assessment

Alternative assessment: Students might participate in rating their peers. Each piece of writing might be read by another student. Or several students might read each piece, and the final rating will be an average of all the student ratings. (If the latter is done, writings might be shared anonymously so students are not influenced by who wrote the piece.)

Submitted By

Melba Smithwick, Paul R. Haas Middle School in Corpus Christi, Texas