Finding a Central Value

When you have two or more numbers it is nice to find a value for the "center".

2 Numbers

With just 2 numbers the answer is easy: go half-way in-between.

Example: what is the central value for 3 and 7?

Answer: Half-way in-between, which is 5.

Mean of 3 and 7

You can calculate it by adding 3 and 7 and then dividing the result by 2:

(3+7) / 2 = 10/2 = 5

3 or More Numbers

You can use the same idea when you have 3 or more numbers:

Example: what is the central value of 3, 7 and 8?

Answer: You calculate it by adding 3, 7 and 8 and then dividing the results by 3 (because there are 3 numbers):

(3+7+8) / 3 = 18/3 = 6

Mean of 3, 7 and 8

Notice that we divided by 3 because we had 3 numbers ... very important!

The Mean

So far we have been calculating the Mean (or the Average):

Mean: Add up the numbers and divide by how many numbers.

But sometimes the Mean can let you down:

Example: Birthday Activities

Uncle Bob wants to know the average age at the party, to choose an activity.

There will be 6 kids aged 13, and also 5 babies aged 1.

Add up all the ages, and divide by 11 (because there are 11 numbers):

(13+13+13+13+13+13+1+1+1+1+1) / 11 = 7.5...

The mean age is about , so he gets a Jumping Castle!

The 13 year olds are embarrassed,
and the 1 year olds can't jump!

The Mean was accurate, but in this case it was not useful.

The Median

But you could also use the Median: simply list all numbers in order and choose the middle one:

Example: Birthday Activities (continued)

List the ages in order:

1, 1, 1, 1, 1, 13, 13, 13, 13, 13, 13

Choose the middle number:

1, 1, 1, 1, 1, 13, 13, 13, 13, 13, 13

The Median age is 13 ... so let's have a Disco!

Sometimes there are two middle numbers. Just average them:

Example: What is the Median of 3, 4, 7, 9, 12, 15

There are two numbers in the middle:

3, 4, 7, 9, 12, 15

So we average them:

(7+9) / 2 = 16/2 = 8

The Median is 8

The Mode

The Mode is the value that occurs most often:

Example: Birthday Activities (continued)

Group the numbers so we can count them:

1, 1, 1, 1, 1, 13, 13, 13, 13, 13, 13

"13" occurs 6 times, "1" occurs only 5 times, so the mode is 13.

How to remember? Think "mode is most"

But Mode can be tricky, there can sometimes be more than one Mode.

Example: What is the Mode of 3, 4, 4, 5, 6, 6, 7

Well ... 4 occurs twice but 6 also occurs twice.

So both 4 and 6 are modes.

When there are two modes it is called "bimodal", when there are three or more modes we call it "multimodal".

Conclusion

There are other ways of measuring central values, but Mean, Median and Mode are the most common.

Use the one that best suits your data. Or better still, use all three!