## SCIENCE OF NHL HOCKEY: Statistics & Averages (Grades 9-12)

##### Objective:

1. Students will be able to distinguish between numerical and non-numerical data. 2. Students will be able to distinguish among the mean, median, and mode of a data set. 3. Students will design and carry out an investigation to collect a set of data and find the mean, median, mode, and range of a set of data.

##### Introduction Notes:

**Science of NHL Hockey: Statistics & Averages**

Subject Area: Statistics, Math, Science

Grade Level: 9–12 (Statistics, Math, Science)

Lesson Title: __Statistics & Averages__

## National Science Education Standards:

## Science as Inquiry: 9–12

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**Common Core State Standards for Mathematics**

Statistics and Probability: 9–12

Suggested Prior Knowledge: concepts of data sets; techniques of collecting data.

Purpose and Introduction: The video uses statistical data collected about NHL goal tenders to give students an understanding of the measures of central tendency of a data set: mean, median, and mode. The activities enable students to apply these concepts to their own data sets.

## Key Vocabulary:

*mean**—*the sum of a set of numbers divided by the number of members of the set*.*

*median**—*the central value in a list of numbers arranged in ascending or descending order; for a set of numbers with an odd number of members, the mean of the two central numbers.

*mode**—*the member that occurs most often in a set of data.

*range**—*the difference between the least member and the greatest member in a set of numbers.

*statistics**—*the scientific application of mathematical principles to the collection, analysis, and presentation of numerical data.

## Objectives:

- Students will be able to distinguish between numerical and non-numerical data.
- Students will be able to distinguish among the mean, median, and mode of a data set.
- Students will design and carry out an investigation to collect a set of data and find the mean, median, mode, and range of a set of data.

**Materials:**

- safety goggles (optional)

- deck of playing cards

- map of community or school district

- meter stick or metric ruler

- graph paper

## Procedure:

1. Review the video with students and elicit from volunteers how to determine the mean, median, and mode of a data set using examples from the video. Introduce the idea of non-numerical data and contrast it to numerical data. Use questions such as the following to prompt discussion:

• What are some examples of non-numerical data?

• Can you find the mean, median, and mode of a set of non-numerical data?

• What are some examples of numerical data from hockey, baseball, or other sports?

• Why is it useful to have a single value (mean, median, or mode) to represent a set of data?

2. Lab protocols should be followed, incorporating safety equipment. If conducted in a science lab, use your discretion on whether or not students are to wear cover goggles.

3. Allow students to examine the materials and then design an investigation that will allow them to collect a data set and derive its range, mean, median, and mode. Consider having students work individually or in small groups and compare their computed values. The following steps describe examples of non-numerical and numerical data, but students should be encouraged to think of others. Use your discretion about whether distance of the students' homes to the school would produce a varied enough data set. If not, they may choose to work with sports statistics researched on the Internet (see Additional Resources). Students might think about using personal characteristics such as height or arm span or birth date, but steer them away from data sets that might be sensitive or embarrassing to a few. Questions such as the following can help focus students’ plans:

• How do you record a set of data?

• What is the first step in finding the median of a set of data?

• What is the mode of a set of data?

• How do you find the mean of a set of data?

• What is the range of a set of data?

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*Numerical and Non-numerical Data*

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4. Remove all face cards and jokers from the deck of cards, and then deal nine cards face up. Record the numbers and suits of the cards on the board as they are drawn. Then direct students to find the mode, median, and mean for the values. If needed, refer to the video to refresh students’ memories. Students could write down the nine cards in increasing numerical order to find the range and the mode for numerical values (if there is a mode) and do calculations to find the median and the mean. Elicit from students whether mode, median, and mean are equal, and whether there is any relationship among them.

5. Next, have students characterize the suits for the set of cards. The suits are non-numerical, so while there may be more than one mode for the suits of the nine cards, there is no mean or median for the suits. Students calculate what percent of cards belong to each suit. (The total should be 100%.)

*Student-Generated Data*

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6. Instruct each student to use the meter stick to measure the distance from his or her home to the school on the map, round it to the nearest centimeter, and write it on the board. Or students can use the map scale to convert centimeters to actual distances. If computers or smartphones are available, students may use map sites or GPS apps to find their distances. Encourage them to use kilometers for distance.

7. Again, have students arrange and analyze the data to find the range, mode, mean, and median of the dataset. Elicit from students whether they expect mean, median, and mode to be equal. Ask questions such as the following:

*When is the median of a data set a better way to characterize the set than the mean?**What percent of values are above the mean?*

8. To follow up this investigation, have students prepare histograms from the distance data (or from hockey or other sports statistics). Have a class discussion on how closely the data resemble a normal distribution.

## Additional Resources:

• http://regentsprep.org/REgents/math/ALGEBRA/AD3/DataTeacher.htm

• http://esa21.kennesaw.edu/activities/stats/stats.pdf

• http://www.sciencebuddies.org/science-fair-projects/project_data_analysis_summarizing_data.shtml

• http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm

• http://www.hockeydb.com/

• http://espn.go.com/nhl/statistics

• http://www.ncaa.com/stats/icehockey-women/d1

**Student Worksheet for Statistics & Averages**

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Experiment Title: _____________________Date: _______Name: ________________________

Student Hypothesis:

Materials:

- safety goggles (optional)

- deck of playing cards

- map of community or school district

- meter stick or metric ruler

- graph paper

Procedure:

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**Data and Observations:**

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**Analysis of Data:**

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**Conclusion:**