Sampling Variation

Our tiny humans are well motivated by sugar, so today we are going look at some issues related to sampling variation, motivated by a sample....err ...snack.

For whom:This activity is good for kiddos learning how to sort and count, up to late elementary kids who are data savvy and don't look at you funny when you say "make me a histogram".

Supplies: 
For this lesson you will need something multicolored to sort: This might be something like a large bag of MnMs candies (or skittles) and a tablespoon,  4 snack pack sized fun bags, or even multi colored beads in a craft stash. (For the record, our home is light on craft stashes. Also, I would be lying if I said these weren't left over from Halloween, so feel free to judge!)

What to do: 

Start with one small bag of candy (or one spoonful/ scoop). Sort the candy by color. Draw a histogram(pictured below) to represent each color. As a pro-tip, if you use lined paper, it is easier for younger kids to have one line represent one candy and keep their columns to scale. In our first sample, you can see there were 4 oranges, 4 greens, one yellow, one red, one brown, and three blues (though one of the blue MnMs is hidden from this angle). 

Some things to point out/ questions to ask: 
Are the colors all represented the equally? Why not? If we opened another bag, would we get the same mix of colors? (Note the foreshadowing here!)

Now, try it again for your second bag:

I recommend making your next histogram above your first one and again use the lines to help keep your scale consistent.

So when we compare our first and second sample, in our second sample we got SO MANY yellows, but not a single brown or red! Spurred on by our variation, we pressed on, opening two more mini bags, and recording our sample a la histogram. After the samples were faithfully documented there was some rebellion in the ranks and the 4 year old retorted "I'm eating my sample so I don't contaminate my next one!"  Halloween candy in March. What could go wrong?

So...what do we see in our data? There is a tremendous amount of variability in the colors that occur in any one pouch. Some pouches don't even *have* all the colors. Some have a ton of one color and a scant few of another.
We decided to make a 'totals' graph for all the MnMs in all 4 of our bags together.

Based on our four bag sample, it's a little hard to believe that they make those colors in equal number. Maybe they don't! If you try this at home, send us a picture of yours in the comments so we can collect more data!


So far, I have shown you the data for MnMs, but, for the sake of science, we repeated the experiment with Skittles. You're welcome. It seems like skittles are far more committed to you 'tasting the rainbow' than MnMs. As you can see in the photo on the right, over a three bag sample, we see pretty consistent numbers of each color. If you are trying to show how samples converge to underlying parameters, I might recommend using skittles, but if you are #teamchocolate, just be prepared for more conversation about sampling!

The big idea of the lesson: Samples are different than their underlying populations. When we look at an individual bag (or tablespoon) of the candies, we see a different pattern of colors when we look at all the candies together. Sometimes colors are evenly distributed and sometimes not, but the larger our sample (or more little samples we put together) the closer we get to the 'true' underlying population.