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…

{*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:

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.

*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:

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.

**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.*

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.