Finding the average (also called mean), median, mode and range can be fun! Here’s an activity I loved doing with my fourth graders year after year. We used the heights of players of an NBA team to practice finding the mean, median, mode, and range.

## Quick Math Review:

__Average/Mean__**: **When finding the mean (which is also called the average), you will add up a list of numbers and divide by the total number of data entries. Perhaps you want to figure out the average height of an NBA team.

** Median**: the middle number (when you order from least to greatest or greatest to least). If there are an even number, you will have two middle numbers. Add them up and divide by 2 (a.k.a. find the average). : )

** Mode**: the most common number in the list

** Range**: the difference between the highest and lowest number in the list

** Outlier**: a number that is much higher or much lower than all the other numbers in the list (an outlier can skew data, so it is good to know if there is one present)

## Math Activity:

Basketball seems like a great sport to choose for this math activity during March Madness, but I'm choosing an NBA team (not a college one) to focus on. You can easily modify this for a team or sport your child, or class, prefers. I’ll be using the example of the Golden State Warriors. If this math activity using a NBA team roster isn’t something your child would enjoy, select a list of data that is of interest to him or her.

1. Choose an NBA Team.

2. Find each player’s roster page on the NBA website (https://www.nba.com/) or find a team roster (https://www.basketball-reference.com/teams/GSW/2020.html or https://www.nba.com/warriors/rosterfor the Golden State Warriors). It will save time to use a team roster, but children love research so you may want them to have the pleasure of looking up each player's height from their roster (or providing a print out) with your supervision (we know it is easy to get distracted).

3. Record the height of each player. Tip: Convert their heights from feet to inches only (I have found that it is much easier to work with inches only, but you can modify this activity to fit your needs). There are 12 inches in a foot so multiply 6 and 12 to find that there are 72 inches in six feet (yes, NBA players are often at least six feet tall). Here’s the list of players for the Golden State Warriors (as of March 9, 2020, using information gathered on March 9, 2020 at https://www.basketball-reference.com/teams/GSW/2020.html).

4. Find the ** average** (also called the

**) by adding up the height of all players and dividing by the number of players.**

__mean__Example:

84+73+81+75+78+77+81+78+76+74+82+78+78+79 = 1,094 inches

Now divide by 12. 1,094/12 = 78.1429 inches

**For the Golden State Warriors, the average height is 78.14 inches **(using information gathered on March 9, 2020 at https://www.basketball-reference.com/teams/GSW/2020.html).

5. Find the ** median** by ordering the list of heights from least to greatest or greatest to least, then locate the middle number.

Example (in inches): 73, 74, 75, 76, 77, 78, 78, 78, 78, 79, 81, 81, 82, 84

Since there are 14 players, we have two middle numbers (78 and 78). Normally we would add the two numbers up and divide by two in order to find the average between them and call it the “middle number.” In this case the two middle numbers are the same, so 78 is the middle number. You can still find the average of the two if you would like to practice: 78+78 = 156.

Now divide 156 by 2 = 78! Yay!

**The median of the heights for the Golden State Warriors is 78 inches (a.k.a. 6 ft 6 in).**

6. Find the ** mode** by seeing which number occurs the most in the list. This is not difficult when you've already ordered the numbers in the set from least to greatest or greatest to least.

Example (in inches): 73, 74, 75, 76, 77, 78, 78, 78, 78, 79, 81, 81, 82, 84

Looking at our list of heights, we see that there are four players who are 78 inches tall and two who are 81 inches tall. The most frequent number is 78.

**The median height of the Golden State Warriors is 78 inches.**

7. To find the** **** range** of the numbers, look at the greatest and least numbers in the list. Subtract the least from the greatest.

84 inches – 73 inches = 11 inches

**The range of the heights for the players is 11 inches.**

I find this to be the most interesting piece of information when doing this project. The tallest and shortest player are less than a foot apart in height! They are all very tall.

8. To find an ** outlier** look at the string of numbers you have been working with. Are there any that are much higher or lower than the others?

Example (in inches): 73, 74, 75, 76, 77, 78, 78, 78, 78, 79, 81, 81, 82, 84

All of the heights for the team are very close together. **There is no outlier.**

Math concepts should be engaging. When we present math with a NBA team roster to a basketball fan, hopefully review and practice are more exciting. There are countless ways we can help practice finding the average, median, mode, and range with children.

## Questions:

Was incorporating basketball with practice in finding the mean, median, mode, and range helpful?

What else could your children find the average (mean) of?

How does working with a list of numbers children are interested in help make the concepts more enjoyable?

## A Song:

Here’s a fun song students love: Mean, median, mode, and range by Dylan Peters: https://www.youtube.com/watch?v=IHginNwss5c

## Fun Facts about the Warriors:

Yes, the Golden State Warriors were previously the Philadelphia Warriors. It seems fitting to focus on this team since they’ve been making history for a long time. March 2, 1962 is the day that Warrior Wilt Chamberlin scored the NBA record 100 points in a legendary game (169-147 win against New York Knicks; photo from https://sportsecyclopedia.com/nba/pwar/phlwarriorsshots.html#images-27)

## More about Mean, Median, Mode, and Range

Here’s a link to Ducksters which will provide more information and examples for these math concepts: https://www.ducksters.com/kidsmath/mean_median_mode_range.php

Another great site to help students understand these concepts is Khan Academy. Here’s a link to a video: https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/measuring-center-quantitative/v/mean-median-and-mode

They also provide practice and feedback for your answers to their questions: https://www.khanacademy.org/math/probability/data-distributions-a1/summarizing-center-distributions/e/mean_median_and_mode

Looking for great websites for kids? Here is a post I shared about __websites educators love, parents want, and children need__. Enjoy!

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