M&M Statistics

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Math: Statistical Probability
Grade Range: Middle School, High School
Format: Hands-on, Stage

This will help students recognize the importance of having a large sample size, and see firsthand how it changes the effects of an experiment.

Contents

Materials

  • Snack-Size Bags of M&M's
  • Whiteboard with Markers
  • Dixie Cups

Safety Precautions

Please read the General Safety section of the Demonstration Safety page before performing this demonstration.

Demonstration

Presentation (Stage)
This stage version of the demonstration works well with small groups of students, but does not work for groups larger than 30 students.
  1. Hand out a bag of M&M's and a dixie cup to each student. Instruct them to open the bags and pour the M&M's into their dixie cups. Make columns on the white board for each of the colors, and ask one student to tell you how many they have of each color. Does everyone have the same set of colors?
  2. Ask four more students to tell you how much of each color they have. Average the numbers from them all, and ask everyone if this is starting to look like a good estimate on colors.
  3. Have all the students tell you how much of each color they have. Average all the numbers, and ask everyone if they think this is a good color estimate. How do their individual bags compare to the whole room's estimate?
Presentation (Hands-on)
  1. Set out six cups, each labeled for a different color, and make the columns on the whiteboard. At the bottom of each column, have the color ratios from 2007 and 1995 listed.
  2. When students come up to the table, ask them to open a bag of M&M's and to sort them by color. Once they do so, have them record the number on the whiteboard. Update the ratio estimates and see how they compare to the old ratios. Did the student's bag fit the current predicted ratio? why or why not?
  3. Students can choose to take the M&M's with them afterwards. As more students come up and record numbers, point out how the numbers will start to balance out and not change as drastically.

Why This Works

Statistical Probability is when you make an educated guess at something based on the number of trials you ran or the sample size you used. As you increase the number of trials, the educated guess will become more and more precise until the changes are minimal, and you have an answer. Likewise, as you increase the sample size, your guess will become more precise until the changes are minimal. In this case, we are trying to figure out the color ratios of the M&M’s in a bag. WE start with a small sample size with a single bag, which gives us a very rough idea on the ratios. By adding a few more bags, we can then get a better idea of what the ratio is supposed to be. The final, large sample size will be much closer to the actual percentages used than the individual sample sizes.

Previous Percentage Ratios for M&M's
Red Orange Yellow Green Blue Brown
2007 13% 20% 14% 16% 24% 13%
1995 20% 10% 20% 10% 10% 30%

Additional Information

  • This demonstration can be done with other candies as well, such as Skittles or gummy bears.
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