Statistical Science: M&M Math
Summary
Introduction
Have you ever wondered weather the outcome of a certain activity is predictable? For example, if you’re randomly picking a chocolate out of a box of mixed chocolates, can you predict how likely it is that you’d end up with a specific type of chocolate, such as a caramel-filled chocolate? To investigate this tasty topic, in this activity you’ll determine the frequency of different colored M&M’s in a package of M&M candies. M&M’s are much cheaper than a box of chocolates and normally come in six different colors: red, green, yellow, blue, orange, and brown. What do you think will be the most, and least, common colors in a typical package of M&M’s?
Background
Often times the frequency of outcomes for an event can be modeled and predicted using statistical analysis. Statistics are facts or data based on a set of numerical information. The set of information is often about a certain group and the statistics are a numerical way to describe that group, also called a “population.” For example, think about a classroom of students (a population made up of a group of students). Some numerical information that could be collected about the population would be the number of boys and girls and the height of each student. This information could then be used to draw certain conclusions about the population, such as the percentage of students who are female or the average height. These facts are statistics about the population.
Many statistics reveal patterns and can be used to make models, form hypotheses, and make predictions about certain things. For example, if you figured out the average height of students in a classroom, that statistic could help you predict the heights of students in other classrooms of the same grade at the same school.
Materials
- At least three packages of plain M&M’s
- Piece of paper and pencil or pen
- Calculator
Preparation
- Prepare a clean, flat surface to empty the M&M’s onto and do some counting.
- On your piece of paper, you may want to create a table to record your results in to make it easier to do your statistical analysis. If you do this, along the top of the paper make columns labeled “Candy Color,” “Package 1,” “Package 2,” “Package 3,” “Total,” and “Percentage.” (Add more columns if you are using more than three packages.) In the “Candy Color” column make a row for each color (by labeling each row “Brown,” “Blue,” “Green,” “Yellow,” “Orange,” or “Red”). Fill out the table accordingly as you do the activity.
Instructions
- Open the first package of M&M’s and carefully empty it onto the cleaned surface. Count the number of M&M’s of each color. How many M&M’s are there of each color? Write the numbers on your piece of paper. (Do not eat the M&M’s before you count them!)
- Open each of the other packages of M&M’s separately and again count the number of M&M’s of each color in each package. How many M&M’s are there of each color in the other packages? Are the numbers similar? Write the numbers on your paper.
- For each candy color calculate the total number in all of the packages combined. What is the total of each M&M color for all packages combined? Write the numbers on your paper.
- Next calculate the total number of all of the M&M’s in all three packages combined. How many M&M’s are there total? Write this number somewhere (it doesn’t need to be on a specific place in your table).
- Lastly calculate the average percentage of each colored M&M per package. Do this by dividing the total number of each M&M color (for all packages combined) by the total number of M&M’s (in all packages combined). For example, if there are a total of 15 red M&M’s and 150 M&M’s total (in all packages combined), you would divide 15 by 150 (which equals 0.10, or 10%). What is the average percentage of each candy color per package? Write the numbers on your paper.
- Look over your results. In an average package of M&M’s, which color is most common? Which color is least common? Do any of the colors have the same frequencies? Do you see any other trends in your data?
Extra: In this activity you used three packages of M&M’s, but your statistical analysis would probably be more accurate if a larger number of M&M’s packages were used. Try doing this activity with at least five more packages of plain M&M’s. How do your results change as you use a greater number of M&M’s packages?
Extra: In this activity you calculated the average number of each candy color for a given package, but what were the percentages like for each package you investigated? You can go back to your data and figure this out. For the packages you investigated, how much variation was there in the percentage of each color between the different packages?
Extra: You could repeat this activity using almost any other product that comes packaged with a mixture of colors, shapes, sizes, or types. Here are some more ideas to try: Skittles, jellybeans, a bag of chips, marbles, trading cards, etc. Can you accurately predict what you are most likely to pick from one of these packages?
Observations and Results
Were there one or two colors that were consistently the most common in each package of M&M’s? Did the most common colors include blue or orange?
In statistics, how often a certain event happens is referred to as the frequency of that event. In this activity, the events investigated were different M&M colors and their frequency was measured by counting their numbers within a package of M&M’s (which was the population investigated). In this activity you most likely found that in an average package of plain M&M’s, the color with the highest frequency was blue or orange (in other words, blue or orange was the most common color). These are generally the most common M&M colors in a plain package, typically making up around 18% to 31% of the M&M’s in a package. (Because the percentages of other colors can be close and there is package-to-package variation, it is possible that this trend was not observed when investigating only three packages of M&M’s.) The color with the average lowest frequency (or, in other words, the average least common color) was probably brown, red, or yellow. There was likely some variation from package to package, and the most common (or least common) color may have been different for different packages.
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Cleanup
- When you’re all done with your statistical analysis, you may enjoy a tasty M&M snack!
Additional Resources
- Statistics, from Kids.Net.Au.
- Relative Frequency, from MathIsFun.com.
- M&M's Color Distribution Analysis, from Joshua F. Madison presents Confusement
- M&M Math, from Science Buddies.
