Mathematics

Averages

We use averages every day and averages are very useful in giving us a picture of what is going on with a lot of information.

Take for example the television programme 2.4 Children.

This is based upon an average. It is because if you look at the number of families in the U.K. and the number of children on AVERAGE, the number of children in each family is 2.4. Notice that you can't get .4 of a child but on average this is the number.

We have different types of average:

 Mean Mode Median

Each has got its strengths and weaknesses. Today we are going to introduce the mean average.

When we talk about average we often mean the MEAN.
The mean average means in the middle.

Here is a short table from the Berkerlies League:

 Team Played Goals for Goals against Fanchester United 12 36 12 Fanchester City 11 33 22 Stroke Rovers 11 22 26

If we want to know what is the average number of goals scored by Fanchester United in every game we do the following:

 Goals for Total played Average = total/ number played Average 36 12 36 /12 =3

Now, you work out the average number of goals scored against Fanchester United.

The answer is 1

Here's how it was done

 Goals against Total played Average = total/ number played Average 12 12 12 /12 =1

That wasn't too bad.

Now you can do that, work out the average (goals for) of the other two teams.

Here are the results

 Team Goals for Total played Average = total/ number played Average = Fanchester City 33 11 33/11 3 Stroke rovers 22 11 22/11 2

The average gives us a picture of what is going on.

Here is a list of the number of goals scored over five games in the season for Stroke Rovers.

 Game Goals for 1 1 2 3 3 3 4 2 5 2 6 1 7 2

Well, what do you think the middle number of the goals scored is?

IT LOOKS LIKE 2!

What do you think the average will be?

Number of games: 7
number of goals: 14
so 14/7 = 2

You will notice that the average always seems to be in the middle.
This is true, the mean average will give us the middle of the numbers we are using.

If we take the smallest number and the largest number, this shows us how spread out the numbers are. This is called the range.

What is the range of these numbers?

 1 3 4 5 8 10

The range is the spread, so the range is 10.

Here is a typical question for mean averages.

If a class of 30 children owned between them 90 pets. How many pets on average would each child own?

Can you work this out?

It is 3 each.
90/30 = 3

This does not mean that each child has got 3 pets, only that the average is 3 each. Just like 2.4 children!

Review

The mean average gives us a picture of a large set of information.
The mean average is always in the middle of our data range.
The range is the spread from the highest to the lowest number we are using.
To calculate the mean we find the total number (the sum) and divide by the number of events.

That is it for the introduction to averages. Next time we will look in greater depth at the mean and introduce the mode.
Good luck!