Average

Oftentimes, when we collect data or measure something more than once, the numbers don't all come out the same.

So what numbers should we use to represent them all?

That's where average comes in.

Here are our three measurements. I'm showing these distances using three bars. Notice how the thirty two bar is the longest, then comes the twenty seven, and the twenty six is the shortest.

The idea of an average is that instead of having three bars of different lengths, we make them all equal. To do that, we can imagine taking a little bit from the thirty two bar and sharing it with the others until all three are the same length.

The average is that common length. If you were to make an estimate, the average must be smaller than thirty two and slightly larger than twenty six and twenty seven.

But how can we find out exactly what the average is?

Well, we can combine all of the lengths together. Think of stacking those three bars end to end. What is the total length?

Let's add those numbers together. Thirty two plus twenty seven plus twenty six. That gives us a total of eighty five centimeters.

Now, since we have three measurements, we want to split that eighty five evenly into three parts. So we divide eighty five by three.

Having a remainder doesn't help when we are thinking about centimeters, so I will add a decimal and calculate the average to the nearest tenth. That equals about twenty eight point three centimeters.

So the average of our three measurements, thirty two, twenty seven, and twenty six is twenty eight point three centimeters. That makes sense with our visual. That's the power of averages. They take uneven measurements and balance them out into one equal value.