M&Ms are one of the all time classics for anyone with a sweet tooth. Most of us first encountered the multicolored candy when we were quite young. Tasting M&Ms as an adult brings back a lot of those wonderful memories of youth. People often think back to mixing up M&Ms with their popcorn while encountering favorite movies for the first time. Others might start grinning as they remember sorting through Halloween candy to find fun size packets of M&Ms.
Everyone has their favorite memories of eating M&Ms. In a similar way, everyone has their own particular favorite color of M&Ms. Some people decide on a favorite solely because of the color. Others insist that different colored M&Ms have subtle differences in their taste. But whatever the reason, it’s common for someone to be just a little bit happier if they reach into a bag and pull out their favorite.
This raises an interesting question. Just what are the chances of any given person pulling out their favorite color of M&Ms? Does every package have the same number of each color or is there some variation on a case by case basis? And is there any way to find some firm statistical evidence to objectively prove the point one way or the other?
A Man of Science on a Colorfully Delicious Mission
A statistician by the name of Rick Wicklin decided to find some firm answers. And as with any great mathematical effort he even made sure to properly document his methodology. Wicklin also held onto an important part of any experimental design. Proper research always requires variables to be minimized and defined to the greatest extent possible. Solid results require solid, as opposed to fuzzy, variables.
When designing a study, the researcher should always have firm answers available when people want to dig further into the methodology. One of the main reasons for this is replication. People should be able to verify a studies results by perfectly replicating even the most minor details involved with it. And Wicklin’s decision to do so turned up some important information for anyone curious about M&Ms packaging.
Not Every Package Is Created the Same Way
Wicklin began his study by using M&Ms from the break room at SAS. Analytics Software and Solutions, or SAS, is well known in certain circles for its impressive and generous supply of M&Ms. If an employee finds himself with a craving for something sweet, he’ll always be able to find a large container of M&Ms in the break room.
Wicklin didn’t want to use up the entire stock of M&Ms at SAS. So instead of counting an entire bin, he took a single sample over the course of late 2016 through early 2017. He found the following numbers with a total size, N, of N = 712.
- Red: 108
- Orange: 133
- Yellow: 103
- Green: 139
- Blue: 133
- Brown: 96
Wicklin then compared these numbers to the last officially published color distribution table. Mars Chocolate stopped listing color distribution in 2008. However, these old numbers would serve as a good metric for a modern count. The new data was consistently different from the old information published by Mars Chocolate. Wicklin noticed one particular point of difference between the old and new data. The green and blue M&Ms were a significant point of divergence between the two. The new samples showed too many blue candies and not enough green.
This doesn’t necessarily prove that the numbers from 2008 were no longer valid. After all, any random sampling has an element of chance within it. A one in a million combination of elements will still happen on occasion even if it’s unlikely.
The Candy Experts Fill In a Few Missing Points
Wicklin decided that he needed to see if he could get some clarification from the manufacturers themselves. The Customer Care team at Mars had a reply for him within a day. They were able to fill in a vital piece of information which impacted the entire foundation of Wicklin’s study.
It turns out that both the plain and peanut M&Ms are produced in two separate factories. And most significantly, the color distribution in each plant is different from the other. To find out which plant a package comes from you simply have to check the manufacturing code. If the code contains the letters HKP then it comes from the Hackettstown NJ plant. If so, then it should have the following distribution numbers.
- Red: 0.125
- Orange: 0.25
- Yellow: 0.125
- Green: 0.125
- Blue: 0.25
- Brown: 0.125
If an M&Ms package’s manufacturing code contains CLV then it’s from the Cleveland plant. If that’s the case, then the numbers will look considerably different than what we see at the Hackettstown plant. The distribution numbers for the Cleveland plant are as follows.
- Red: 0.131
- Orange: 0.205
- Yellow: 0.135
- Green: 0.198
- Blue: 0.207
- Brown: 0.124
The differences between green and blue are of particular note when looking at Wicklin’s findings. It appears that SAS was sourcing the majority of its stock from the Cleveland plant. However, there was just enough of the Hackettstown plant’s packages to skew his numbers.
Final Results From the Study
Wicklin was able to verify that packages from the two plants did in fact match with the numbers he received from the Mars Customer Care service. He was also able to confirm that the last officially published data from Mars, back in 2008, was no longer accurate.
At first glance this information might just seem like an amusing diversion. However, Wicklin brings up an important point about M&Ms distribution. Teachers often struggle to find ways to really connect their students to the class’s subject matter. This is especially true for the often abstracted subject matter found in statistics. It’s quite common for teachers to search out ways to help highlight real world use of these concepts. And one of the best ways to do so is through something as colorful and delicious as M&Ms. This has led to countless teachers grabbing bags of M&Ms for their class.
But without a firm understanding of the underlying statistics, a teacher may well be setting up an unsound foundation. To really teach statistics, an instructor needs to be able to answer questions about any given exercise. Until Wicklin’s study, this really wouldn’t have been possible when using M&Ms as a teaching aid.
Wicklin’s study now gives teachers the ability to accurately predict the statistical probability of any given color appearing in batches of M&Ms. This, in turn, ensures that students can replicate Wicklin’s own findings as part of their larger educational experience. The colors of M&Ms are certainly a fun part of opening up a new pack. But this study shows that even the most light-hearted moment can help people learn about the amazing and colorful world we’re all living within. It can also give the average person a moment of reflection on the many ways in which science and beauty coexist.
