Dad Blogs: Fun and Surprising Statistics for Kids


Setting up the experiment

There is an interesting little puzzle called the Monty Hall problem that is a great way to introduce statistics for kids. There are different ways to present the problem (one requires goats), but for our kids, we used three cups and M&Ms. The kids (and Lily’s doll) took turns hiding one M&M under one of the three cups. We asked Mama to pick one of the cups. Before lifting the cup, we pick up one of the other cups and reveal that it does not have an M&M underneath. Is it to Mama’s advantage to switch her original choice?

MaryAnne’s intuition (as well as most people’s intuition) is that it doesn’t matter—that there is just a 50% chance of being right or wrong—so we decided to play a game to test her hypothesis. If MaryAnne’s original guess is right, she gets to keep the M&M; otherwise the kids get to keep whatever is under the other cup. To keep track of our data, we collected the M&Ms on a piece of paper with an area for “Mama” and an area for “Kids”. The kids loved getting high-fives and adding the M&Ms to their pile as the experiment progressed, but it was a little difficult to keep the kids from eating our data.

celebrating their win

Much to Mama’s disbelief (and to the kids’ great excitement) the kids got a little over twice as many M&Ms!

The final score

I didn’t go over the mathematical proof that you are expected to do twice as well if you switch, but it did get the kids excited about counting!

By the way, interested readers can play a version of the game with goats here.

Comments

  1. says

    What a great hands-on game! I bet all of you will remember what you learned (to switch!).

    I love seeing the kids’ posters on the wall behind them as well! :)
    .-= Elisa | blissfulE´s last blog ..a cooler place to be =-.

  2. Mike says

    @Catherine: Yeah, it drives nearly everyone crazy. Apparently, when the problem appeared in a magazine a while back, approximately 10,000 readers (including those with PhDs), wrote in claiming the switch strategy was wrong. It was reassuring to have the M&Ms validate the mathematics since it is so counterintuitive. :-)

  3. says

    We did this in our statistics class in college, I’ve done the proof, but I STILL don’t “Believe” it! Clearly I need to do the M&M experiment to get my hind-brain to buy in.

  4. says

    M & M’s make anything fun and worth learning about:-). Both you and Mike are so smart and are raising some super intelligent children! I am always impressed with what you teach them and the ways you go about it.

  5. says

    Love the M&Ms! Definitely a math motivator… goats, not so much. I had a goat as a kid. They are a headache :) Thanks for sharing this one. My son loves games and he is getting to be a good little counter!

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