M&Ms Statistics Saturday Science Club

M&Ms Statistics

Author: Louis Varriano

Activitiy Description

The following experiment teaches students how to calculate and use a statistical average, using M&M candies as a tangible and delicious object. A YouTube video is first used to demonstrate what an aver- age is and how it is useful.

Goals/Objectives

• To teach students what a statistical average is and how to calculate it • To teach students about recording experimental data • Toshow students how an average can help predict the distribution of a given sample (i.e. predict the number of each color candy within an M&Ms packet)

Needed Supplies

• 1 ''fun-sized'' packet of regular M&Ms for each student ( can be used for students with dietary restrictions, with purple Skittles being equated with brown M&Ms - the data can be ex- cluded or kept, as it will not affect the results much) • 1 larger M&Ms package • pencils for each student • graph paper to create a bar chart • colored pencils, markers, or crayons for the bar chart

Experiment Steps

1. Pull up the YouTubevideo listed in the Sources section. Have students silently count the number of times that ''Alan'' and ''Steve'' are said as the video plays. Play the video only once.

2. Record students' counts on the board. Students should have a variety of responses with some above and some below the true number. Explain to students that we can calculate an average to find a good estimate when we have unreliable data. Show students how to take an average and do so for each name.

3. Play the video again and count as a class to find the true number of times the names are said. Does the average you found match? Is it close?

4. Pass out a packet of M&Ms to each student. Have students open their packets and count the number of each color of M&M within the packet.

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5. Using the graph paper, have students make a bar chart of their M&Ms by color. Make sure to include labels on both axes and a title.

6. Record each students' results. You should record the number of each color as well as the total number of M&Ms in each packet.

7. Calculate the average number of each color per packet by adding up all M&Ms of a single color, then dividing by the number of packets. Also calculate the average number of M&Ms per packet.

8. Do students have more or less than the average for each color? Explain to students what an outlier is. Do any students have any outlier packets?

9. Explain to students what a percentage is and how to calculate it. Calculate the percentage of each color of M&Ms, using the combined packet data.

10. Now explain to students that statistics allows us to predict the percentage of M&Ms by color in the larger packet of M&Ms. We would expect the smaller and larger packets to have about the same percentage of each color.

n.b. We assume that the candies are manufactured together in set percentages and just packaged into different-sized bags. This is likely untrue, but the assumption is fine for the purposes of the exercise. Inquisitive minds may ask about this point.

11. Open up the larger package and count the number of M&Ms of each color. It is probably a good idea to have done this beforehand. Find the percentage of each color. Are your predictions close?

12. You can compare your results to the official statistics given by the Mars company[2]. Does their company do a good job of quality control?

13. Students can eat their experiment once finished!

Questions to Ask

1. What are some other examples we can use averages for? Literally anything countable. Averages are great for all sorts of statistics and for getting a feel of a situation. They do not capture outliers well and can be very skewed by their presence.

See the Experiment Steps for more questions to ask.

References and More Information

1. https://www.youtube.com/watch?v=aXqkNF8fgs8 - video to use in the experiment

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2. Email from Mars North America to Louis Varriano (copied below).

Dear Louis:

Thank you for your email regarding M&M'S® Chocolate Candies.

Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect.

On average, our mix of colors for M&M'S CHOCOLATE CANDIES is:

M&M'S : 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown.

M&M'S PEANUT: 23% cyan blue, 23% orange, 15% green, 15% bright yellow, 12% red, 12% brown.

M&M'S KIDS MINIS: 25% cyan blue, 25% orange, 12% green, 13% bright yellow, 12% red, 13% brown.

M&M'S DARK: 17% cyan blue, 16% orange, 16% green, 17% bright yellow, 17% red, 17% brown.

M&M'S PEANUT BUTTER and : 20% cyan blue, 20% orange, 20% green, 20% bright yellow, 10% red, 10% brown.

M&M'S PRETZEL: 28.5% blue, 14.3% each of yellow, orange, green, brown and red.

Each large production batch is blended to those ratios and mixed thoroughly. However, since the individual packages are filled by weight on high-speed equipment, and not by count, it is possible to have an unusual color distribution.

Have a great day!

Your Friends at Mars Chocolate North America

Case ID 40907857

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