Overview

Students play a card game to determine whether mean, median, mode or range will give them the highest result.

Objective

Students will be able to estimate and compute mean, median, mode and range.

Standards Addressed

Mathematics — Data Analysis and Probability

Grade 4

Statistical Methods. Benchmark E

07. Identify the median of a set of data and describe what it indicates about the data.

08. Use range, median and mode to make comparisons among related sets of data.

 

Grade 5

Statistical Methods, Benchmark F

06. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data.

 

Grade 6

Statistical Methods, Benchmark F

04. Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).

 

Grade 7 (Enrichment Activity)

Data Collection, Benchmark A

01. Read, create and interpret box-and-whisker plots, stem-and-leaf plots and other types of graphs, when appropriate.

Statistical Methods, Benchmark F

03. Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures.

 

Grade 8

Statistical Methods, Benchmark D

04. Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles).

Materials

• One deck of cards per pair students

Procedure

1. Give each pair of students a deck of cards. Ask them to take out all of the face cards so that they will only keep the cards ace through 10.

2. Distribute to each pair of students the handout What’s the Deal: Mean, Median, Mode and Range.

3. The goal of the game is to get the highest score at the end of the time period.

4. Review mean, median, mode and range and how to calculate each.

5. Before the students play, ask each to player specify which measure they would expect to have the highest total after five or 10 sets of numbers have been drawn.

6. Have each pair of students deal out seven cards and list the numbers that are dealt. Then instruct them to compute the mean, median, mode and range, and record the data on the handout.

7. Students could repeat the exercise as man as 10 times, depending on how much class time you have. The students need to shuffle the cards each time before redealing them.

8. Have the students exchange papers between groups to check the accuracy of their answers.

9. Any student who selected the correct column as being the highest can enter his/her score to see who the classroom winner is (the person with the highest score).

10. Enrichment: Depending upon the amount of time available, you could gather classroom data from each group for each item and make box-and-whisker plots with the composite data. Students can then write the results of the experiment using the information from the box-and-whisker plot.

11. Students can write about why range will often give them the highest score.

12. Extension: Have students complete the handout Measures of Center and Spread.

Answers

Mean Health Care Salaries

1. Mean — $56,531.67

2. Median — $34,855

3. Mode — No Mode

4. Range — $163,190

5. The median is a good measure because the very large salary of surgeons skews the data and makes it much higher. The best measure often depends on the purpose of its use.

 

Income Problem

1. Mean — $33,250

2. Median — $24,500

3. Mode — $21,000

4. Range — $84,000

5. The owner would use the mean because the average salary would be higher.

6. The union leader would use either the median or the mode. The median would show that half of the people make less than $24,000. The mode would show that half of the people earn only $21,000.

7. The statistician would use the median. It shows that half receive more than the median and half earn more.

Evaluation

For 10 groups of data
There are 10 groups with four answers for each group and four totals. Students could receive a point for each correct answer plus six bonus points if either partner selected range as their guess of what would give them the highest score for a total of 50 points.

For five groups of data
There are five groups with four answers for each group plus four totals. Students could receive two points for each correct answer plus six bonus points if either partner selected range as their guess of what would give them the highest score.