## Saturday, February 18, 2017

### Total Amount of Skittles: Fixed or Variable?

Today, I read a great post from Dan Meyer talking about a 3-Act lesson he did in an elementary school having students estimate the total number of Skittles in a jar. A statement he made got me thinking about the variability or fixed nature of the total.

Here's Dan's post: A High School Math Teacher’s First Experience Teaching Elementary School

To summarize, here's the setup: you use a large number of "fun" size of packets of Skittles and add the contents to a jar. Sounds fun. You fill the jar to capacity. How many Skittles, in total, are in the jar? Oh, this is fun.

The average number of Skittles in each of these individual packets is 14 candies (I think). Of course, we should expect some small amount of variability of the number in each packet. Some packets may have 13 (sad) and some lucky ones might even have 15.

Let's assume there are a fixed number of packets with a variable number of Skittles between the packages. My question is: Will the total number of Skittles in the jar always be a fixed amount or will it, too, be variable?

Idea 1: The total number of Skittles will be fixed. Perhaps, the unbiased nature of the samples will make it so that total = average (of 14) x number of packets.

Idea 2: The total itself could also be variable. It's possible that the individual variability of the packets is large enough that it might make the total not constant.

Any thoughts on each of these ideas? Or both? Is there an idea 3? This is a fun statistical question.

P.S. You can find lots of fun statistical activities using Skittles. I just like eating them.

(Photo from Sweet Factory.)