MEAN FROM FREQUENCY TABLE

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 + 1×52 + 5 + 4 + 2 + 1

And now we calculate:

Mean = 2 + 10 + 12 + 8 + 514
=  3714  =  2.64...