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Statistical Science: Melt-in-Your-Mouth Math

A prediction project from Science Buddies
bsh m&m math statistics



George Retseck

Key concepts
Mathematics
Statistics
Probability
Prediction

Introduction
Have you ever wondered what outcomes are predictable? For example, if you're randomly picking a chocolate out of a box of mixed selections, can you predict how likely it is that you'd end up with a specific type of chocolate, such as a caramel-filled candy? To investigate this tasty topic, in this activity you'll determine the frequency of different color M&M's in a package of M&M candies. Standard M&M's 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, the frequency of outcomes for an event can be modeled and predicted using statistical analysis. Statistics are facts or data based on known 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 individuals). Some numerical information that could be collected about the population would be the numbers of boys and girls, along with 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 average height. These facts are statistics about the population.

Many statistics reveal trends, which can be used to 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 average height of students in other classrooms of the same grade at the same school.

Materials
• At least three standard-size (47.9-gram) packages of plain M&M's
• Piece of paper and pencil or pen
• Calculator

Preparation
• Prepare a clean, flat surface on which there is room enough for you to empty the M&M's packages and make separate piles of each color candy.
• On your piece of paper you might want to create a table to record your results; this will 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.

Procedure
• Open only 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 in your record table. (Do not eat any of the M&M's before you finish the activity!)
• 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? Record the numbers in your table.
• For each candy color calculate the total number from all of the packages combined. What is the total of each M&M color for all packages combined? Write the numbers in your table.
• 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 color M&M. 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 (in all the packages) and 150 M&M's total (in all packages combined), you would divide 15 by 150 (which equals 0.10, or 10 percent). What is the average percentage of each candy color? Write the numbers in your table.
• Look over your results. In an average package of M&M's, which color would you predict to be the most common? Which color would you predict to be the 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 calculated the average number of each candy color, 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: 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 packages?
Extra: You could repeat this activity using almost any other product that comes in a mixture of colors, shapes, sizes or types. Here are some more ideas to try: Skittles, jelly beans, a bag of chips, marbles, trading cards, etcetera. 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? What does this say about the likelihood of randomly selecting one of these colors versus a less common color when reaching into a package of M&Ms?

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 packages of M&M's, (which was the population investigated). Here you most likely found that in a package of plain M&M's the color with the average 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 package of the plain variety of the candies, typically making up around 18 percent to 31 percent 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 least common color) was probably brown, red or yellow. There was likely, however, some variation, and the most (or least) common color may have differed from package to package.

Cleanup
When you're all done with your statistical analysis, you may enjoy a tasty M&M snack! And don't forget to share with friends and helpers.

More to explore
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

This activity brought to you in partnership with Science Buddies
ScienceBuddies

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