Archive for the ‘counting’ Category


Sunday, March 18th, 2007

Statistically analyzing the color distribution of M&M’s is apparently a not too uncommon exercise to help students learn about probability, averages, and other useful statistics. I was first exposed to this activity while taking a statistics class at my college, but it’s a useful tool for anyone to learn these concepts. It’s also one of the few learning activities you can eat when you’re finished, which is never a bad thing.

I recently came into possession of two 14 ounce bags of Dark Chocolate M&M’s. Before I ate them I decided to see what the breakdown of colors was, and to see what other information that I could extract from them, useful or not.

Here’s what I discovered:

Searching the official M&M’s site(sound warning) turned up the following information on the breakdown of colors:

“Brown – 17%, Yellow – 17%, Red – 17%, Blue – 17%, Orange – 16%, Green – 16%”

I had two “Medium Size Bags” of Dark Chocolate M&M’s. Medium Size in this case means a bag of 14 ounces. I don’t actually have a scale, so I had to take the word on the packages that they did indeed each contain 14 ounces of M&M’s. Including broken pieces Bag 1 had 462.5 M&M’s and Bag 2 had 466 M&M’s Giving us a grand total of 928.5 M&M’s. Dividing the number of M&M’s in the bag by the number of ounces on the bags gives us 33.04 M&M’s/oz for Bag #1, 33.29 M&M’s/oz for Bag #2, or an average of 33.16 M&M’s/oz.


Next I decided to look at the breakdown of the colors to see what distribution of colors the manufacturer determined was aesthetically pleasing. My counting results are in the following table:

  Bag #1 Bag #2 Total
Red 62.5 71.5 134
Orange 80 82 162
Blue 78 76 154
Brown 78.5 82.5 161
Green 78.5 64 142.5
Yellow 85 90 175
Totals 462.5 466 928.5

So, what does that mean? Well, by itself, not much yet, so let’s throw some more math at it.

The following table shows the percentage of each color in each bag, and then the overall percentage of each color.

  Bag #1 Bag #2 Overall
Red 13.51% 15.34% 14.43%
Orange 17.30% 17.60% 17.45%
Blue 16.86% 16.31% 16.59%
Brown 16.97% 17.70% 17.34%
Green 16.97% 13.73% 15.35%
Yellow 18.38% 19.31% 18.85%

Putting the data into delicious pie-form yields the following three graphs:

Most of these percentages are reasonably close to the above-mentioned distribution (Brown – 17%, Yellow – 17%, Red – 17%, Blue – 17%, Orange – 16%, Green – 16%). However, there are a few anomalies: Red is consistently low, Green is inconsistent but averages low, and Yellow is significantly higher than the 17% reported by the website.

So far, so good, but I felt the need to proceed further to unlock other secrets this mountain of treats held, so I pressed on, and threw another graph at it.

Dividing the number of M&M’s I counted in each bag by the weight printed on the bags told me that there are approximately 33 candies in one ounce of M&M’s. Using the percentages calculated above, any one ounce will have colors in roughly the following quantities:

  Bag #1 Bag #2 Overall
Red 4.46 5.11 4.79
Orange 5.71 5.86 5.79
Blue 5.57 5.43 5.5
Brown 5.61 5.89 5.75
Green 5.61 5.89 5.75
Yellow 6.07 6.43 6.25

From this we can extrapolate that a ‘small bag’ (1.79 ounces) of Dark Chocolate M&M’s will have an approximate breakdown as follows:

Small Bag
Red 8.57
Orange 10.36
Blue 9.85
Brown 10.29
Green 9.11
Yellow 11.19

Needlessly extracting further information tells us that, given the admittedly small sample size, when reaching into a new bag of Dark Chocolate M&M’s your chances of pulling out a specific color can be approximated by the table below:

Chance of Pulling out One Color
Red 14.43%
Orange 17.45%
Blue 16.59%
Brown 17.34%
Green 15.35%
Yellow 18.85%

Could we go further? Of course! The sky’s the limit, really. I just ran out of fun graphs to try. Feel free to take my sample data and compare it with your own, or do anything you want with it. Copy it, teach with it, grade it and tell me what I did wrong. Just drop me a line to let me know where it ends up.