“They all taste the same”

This week in class, my 4 stat classes consumed almost 2,000 M&M’s in the name of statistics.

Here’s the breakdown, by color (the percentages next to the colors denote the average breakdown according to M&M/Mars):1

The point of the exercise, of course, is to compare our observed counts of each color to see how well they match the expected proportions, by way of a chi-squared goodness-of-fit test.

Of course, some smart guy chimes in with:

Why don’t they just make all of the percentages the same? They all taste the same…

To which I asked,

When you go shopping for a car, don’t you care what color it is?!2

To which another smart guy had to retort:

Those all taste the same too.

-_-

Perhaps ironically, Skittles are supposedly manufactured with equal proportions of each color… even though those taste different.

Yesterday was my birthday, and I came dangerously close to taking my first sick day of the year.3

Apparently the officers of Mu Alpha Theta4 were going to get me cake, but when they clearly saw that I was having trouble just sitting up straight, brought me this instead:

1. If you’re curious, here are the breakdowns for the different types of M&M’s:

   M&M’S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown.

   M&M’S PEANUT: 23% cyan blue, 23% orange, 15% green, 15% bright yellow, 12% red, 12% brown.

   M&M’S KIDS MINIS: 25% cyan blue, 25% orange, 12% green, 13% bright yellow, 12% red, 13% brown.

   M&M’S DARK: 17% cyan blue, 16% orange, 16% green, 17% bright yellow, 17% red, 17% brown.

   M&M’S PEANUT BUTTER and ALMOND: 20% cyan blue, 20% orange, 20% green, 20% bright yellow, 10% red, 10% brown.

   M&M’S PRETZEL: 28.5% blue, 14.3% each of yellow, orange, green, brown and red.

   M&M’S COCONUT: 37.5% white, 37.5% brown and 25% green.

   The company also adds:

   “Each large production batch is blended to those ratios and mixed thoroughly. However, since the individual packages are filled by weight on high-speed equipment, and not by count, it is possible to have an unusual color distribution.” [↩]

2. I was trying to make the point that consumer preferences — which is what the company supposedly bases these proportions on — count for a lot [↩]
3. Haven’t taken one of those since the Lakers were NBA champs [↩]
4. which I help co-sponsor [↩]