Oct 02

The Average Bears: Mr. Mean, Mr. Median & Mr. Mode

by Hannah Holt »


Last week, my son asked me, “What does average mean?” I thought it was an interesting question, socially and mathematically.

Averages look at groups of things (or individuals) and point out what’s common, normal, or ordinary.

As you can probably tell from this loosey-goosey definition there is more than one way to find an average. So how do you find an average? To help us out, I want to introduce you to a few bears. First there is Yogi. He is…

smarter than

{Image: http://en.wikipedia.org/wiki/Yogi_Bear, text added}

Then there are Mr. Mean, Mr. Median, and Mr. Mode. They are your average bears:

Mean Median Mode

One day, Yogi Bear wanted to know how the squirrels in Jellystone Park were doing. He called for Mr. Mean, Mr. Median, and Mr. Mode and said:

Yogi: Go find out how the average squirrel is doing.

Mr. Mean went to Squirrel Tree first. The squirrels had differing amounts of acorns.

squirrels and acorns

Mr. Mean is mean. He took all their acorns and counted them. There were seventy acorns and seven squirrels. He divided all the acorns into seven piles. Each squirrel got 10 acorns:

squirrels and acorns mean

This made some of the squirrels happy and some mad! Mr. Mean went back to Yogi and said:

Mr. Mean: The squirrels are great. The average squirrel has 10 acorns.

But after Mr. Mean left, the squirrels who lost acorns took them back. So all the squirrels had the same number of acorns as before.

Mr. Median went to Squirrel Tree second. Mr. Median loves the middle. He found the squirrel with the middle amount of acorns and reported this number to Yogi.

squirrels and acorns median

Mr. Median: The squirrels are okay. The average squirrel has 7 acorns.

Finally Mr. Mode went to see the squirrels. Mr. Mode loves whatever happens most often.

squirrels and acorns mode

He came back and said…

Mr. Mode: The squirrels are terrible!!! The average squirrel only has one acorn.

Whom should Yogi Bear believe? He sent the Three Average Bears to Squirrel Tree and they all came back with different answers. What do you think is the best average?

Three Ways to Find an Average:

1. Mean: Add up all the parts and divide by the number of pieces. (40+12+8+7+1+1+1)/7 This is the most commonly used average.

2. Median: Arrange all the numbers from most to least. Pick the middle number. If you have an even number of data, take the mean of the two middle numbers.

3. Mode: Look through all the numbers and count how often each number happens. Pick the number that happens most often.

Note: As an engineer, I often faced situations with more than one “right” answer. A good engineer can usually make the numbers say almost anything. However, a great engineer uses her judgement to find the best and most accurate way to present the data. Some clients pressure you to give them the answers they want. However, this never pays off in the long run. Someone could get hurt. And even if no one gets hurt, someone else is bound to look at the data later. If they find data splicing, your client could get sued and lose more money than if you had told them the truth. Also, you could lose your licence for bad engineering practice. Engineering is more than number crunching; it’s about being honest and using good judgement.

  1. Susanna Leonard Hill

    Wow! Math as a story! I would have like it a LOT more in school if it was presented like this :) So clever, Hannah! :)

    • Hannah Holt

      :) Thanks, Susanna.

  2. Evelyn

    We love this post! K-Pants says: \\\\\\\\\\\\\\\\\

    Which means, “I love bears.” Also, I think this is ingenious!

    • Hannah Holt

      “DJLIJGN” That means, I’m so glad K-Pants approves!

  3. Romelle Broas

    I just had an idea! I am going to start sharing your educational post via email to my kids. They are at the age where they respond well to email. Even if they are older, this concept could sit well in their heads with your amazing and fun explanation.

    I used to tell them about it, but I think having them click on the link themselves will be more productive.

    • Hannah Holt

      Wonderful! I hope your kids enjoy it. :)

  4. Gramma Holt

    I love your brain! Ii would never had thought of explaining a word with different meanings in such a clever way…..not just kids would appreciate this approach. I love your brain. I want your brain, but I know it is better off with you because you use it more than I would. More brainy stories, please…..

    • Hannah Holt

      Right now my brain hurts. :) I think we’ll do something a little more light and fun next week. But we’ll do more like this again soon.

  5. Cathy Ballou Mealey

    “Boo Boo, you’ve tried to stop my brilliant ideas with common sense a thousand times. Has it ever worked?”

    Love you Yogi! Smarter than average indeed.

    • Hannah Holt

      I was very tempted to include Boo Boo, but thought that might be one too many bears. :)

  6. Erik - This Kid Reviews Books

    Don’t forget the forest RANGEr (who, in this case, got 39)! To get range, I subtract the lowest (1) from the highest (40) and you get the range (39) :)

    • Hannah Holt

      Good one, Erik! You are a clever kid. Perhaps we should also have an OUT(lier) HOUSE for the number 40 because it’s so far away from the others. You are a statistician in the making.

  7. Rebecca

    Love this! Passing it along to our math teacher leader and 5th grade team!

    • Hannah Holt

      Fun! I hope s/he enjoys it.

  8. Tina Cho

    Sounds like another great math story to be made into a pb!