Food Counts

By Ivars Peterson

Muse, September 1999, p. 34.

You tear open a package of M&M's chocolate candies. Fifty-seven little candies spill out. You notice right away that certain colors are more common than others. In fact, you might count 7 brown, 17 red, 18 yellow, 6 green, 5 orange, and 4 blue candies in this bag. Does every package contain exactly the same amount of each color?

A second package turns out to hold 55 candies: 12 brown, 12 red, 13 yellow, 9 green, 7 orange, and 2 blue. You can see that packages don't necessarily contain the same number of candies. And the number of each color can be different, too. At the same time, you can see hints of a pattern. For example, there are fewer blue candies than red ones. To investigate further, you can open a few more packages, or, better yet, team up with your friends to check out even more. You can then add together the counts for each color and calculate what percentage of the total number of candies each color represents.

Mars, the maker of M&M's, says that it produces the colored candies in the following proportions: 30 percent brown, 20 percent red, 20 percent yellow, 10 percent green, 10 percent orange, and 10 percent blue. The different colors are then all mixed together before packaging. In a perfect bag of 50, you'd have 15 brown, 10 red, 10 yellow, 5 green, 5 orange, and 5 blue.

How do your counts compare with the official figures?

If you were blindfolded and picked about 50 candies out of a huge vat of mixed M&M's, you'd probably get different results each time. On the other hand, if you were to check all the colored M&M's in the vat, you would get figures that exactly matched what went into the vat in the first place. In general, the more samples you took from the vat, the closer you would get to those original numbers.

Once in while, you may find that your counts are off even when you have checked a lot of packages. This could mean one of two things: either the vat wasn't mixed very well, or the company changed the color proportions.

So what do you do with all the candies once you've counted them? You can probably figure out the answer to that question pretty easily. Sampling M&M's is a tasty case of having your data and eating it, too.

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