The Mean from a Frequency Table

It is easy to calculate the Mean:

Add up all the numbers,
then divide by how many numbers there are.

But sometimes we don't have a simple list of numbers, it might be a frequency table like this (the "frequency" says how often they occur):

Score	Frequency
1	2
2	5
3	4
4	2
5	1

(it says that score 1 occurred 2 times, score 2 occurred 5 times, etc)

We could list all the numbers like this:

Mean = 1+1 + 2+2+2+2+2 + 3+3+3+3 + 4+4 + 5(how many numbers)

But rather than do lots of adds (like 3+3+3+3) it is easier to use multiplication:

Mean = 2×1 + 5×2 + 4×3 + 2×4 + 1×5 (how many numbers)

And rather than count how many numbers there are, we can add up the frequencies:

Mean = 2×1 + 5×2 + 4×3 + 2×4 + 1×5 2 + 5 + 4 + 2 + 1

And now we calculate:

Mean = 2 + 10 + 12 + 8 + 5 14  
=  3714  =  2.64...

And that is how to calculate the mean from a frequency table!

Here is another example:

Notation

Now you know how to do it, let's do that last example again, but using formulas.

This symbol (called Sigma) means "sum up" (read more at Sigma Notation)

So we can say "add up all frequencies" this way:

(where f is frequency)

And we can use it like this:

Likewise we can add up "frequency times score" this way:

(where f is frequency and x is the matching score)

And the formula for calculating the mean from a frequency table is:

So now we are ready to do our example above, but with correct notation.

There you go! You can use sigma notation.

Calculate in the Table

It is often better to do the calculations in the table.