Individual Posts: M&M Statistical Analysis
Professors Judy Williams and Mario Scribner, Math 240 (Statistics),
Tidewater Community College, reproduced by D. Reiss with permission


  • Step 1: Buy a King Size 3.14 oz or larger package of Plain M&Ms.
    1. Create a Bar plot below for the distribution of colors.
    2. Count the number of each color and find the modal color.
    3. Calculate the percentage of each color in a package by taking the number of each color and dividing by the total number of M&M’s in a package.
    4. Record these percentages above the appropriate color on your bar plot.
    5. Using the relative frequency approach estimate the probability of selecting a blue M&M.
  • Step 2: Share the information from the M&M count you did in Step 1. Respond by 11:59 p.m. Wednesday, since this is information you already have. Then return for Step 3 instructions.
  • Reply to this message. Change the Topic line to read:
    Total=___ Blue=___ Percent blue=___
    where Total is the total number of candies in your bag, Blue is the number of blue candies in your bag, and Percent blue is -- do I need to say this? -- your blue/your total (100)

  • Step 3: Find the total m&m candies counted by the class and the total blue candies counted. By the way, M&M/Mars Company states that M&Ms contain 10% blue candies.
    1. Calculate the percent blue m&m candies for the class.
    2. Compare the class percent with your percent.
    3. How does this exercise illustrate the Law of Large Numbers
graphic-m&m candy + link to website

Selected Student Responses

Step 2

Total = 104, Blue = 11, Percent Blue = 10.6%
Total=106 Blue=7 Percent blue=6.6%
Total=286 Blue=36 Percent Blue= 12.58
Total=100, Blue=12 Percent Blue=12% I just wanted to say: no, I did not eat any M&M's until I was done counting, ha-ha! I actually got exactly 100 Plain M&M's. My money's worth was missing a few more, hee-hee! :) Take care all!
Total=106, Blue=20, %Blue= 18.9%
Total=107 Blue=8 Percent=7.5
Total= 101, Blue= 18, % Blue= 17.8% I kind of feel short changed a few M & M's. I also feel fat thinking that I can eat 101 M & M's in less than 5 minutes!

Step 3

Total M&M's for the class = 2602
Total Blue M&M's = 303
Percent Blue = 11.6%
My was slightly higher but very close. (12.58%)
The percentage of blue in a small sample (my bag) is about equal to the percentage of blue in a large population.

1. There are 2702 total pieces of M&M's.
2. The are 11.5% Blue (312) Blue M&M's
3. The class results vary so drastic, I cannot accurately judge. However, compared to the majority, it looks comparatively similar.
4. The experiment compares to the Law of Large Numbers because after the experiment was repeated over and over, the numbers start to average out to become closer to the stated, or observed, outcome.

1. total m&ms (class) = 2598
total blue (class) = 309
2. percent blue (class) = 11.89%
3. my percent: 20/103 = 19.4%
My percentage doesn't jive very well with the rest of the class. I must have gotten and outlier bag, but if averaged w/ John's bag, it approaches the class average. (Sorry, John, I guess I got your blue ones). The more observations you take, the closer you'll get to the actual average.

Total M&Ms = 2702
Total Blue M&Ms = 312
% Blue M&Ms = 11.55%
I had over the percentage in my bag (18.9%), but I can see how the law of large numbers applies. The more M&Ms we counted (larger the sample), the closer we got to the actual probability obtained by relative frequency, which the company stated was approximately 10%.

Total M&M's for the class = 2705
Total Blue M&M's = 327
Percent Blue M&M's = 12.09%
My percentage of Blue M&M's = 10.58%
Since the individual experiments ranged from 2.88% to 20%, and the class average is 12.09%, we, collectively, approached the theoretical probability of 10% which illustrates the Law of Large Numbers.

I have never seen so many different counts and mine is different as well. I had to subtract 104 M&M's as John's was posted twice. This is my count.
1. There were 2,598 M&M's counted by the class.
2. Of the 2,598 M&M's, 281 were blue.
3. The class percentage of blue M&M's is 10.8%.
4. This computes to a percentage of 10.8% which is fairly close to the 10% quoted by M&M Company.
5.These calculations come fairly close to the theoretical probability, which would support the "Law of Large Numbers."