Step by step
The question
Question: find the mean of this frequency table.
The values x are 4, 5 and 6.
Their frequencies f are 5, 10 and 5.
x is the value.
f is how many times it comes.
So 4 comes 5 times.
1 Multiply x × f
A new column: x times f.
It is the total of each row.
4 comes 5 times: 4 × 5 = 20.
5 comes 10 times: 5 × 10 = 50.
6 comes 5 times: 6 × 5 = 30.
2 Add the columns
We add the f column: 20 numbers in all.
We add the x × f column: the total of all the numbers is 100.
3 Share equally
The mean shares the total equally: 100 divided by 20.
Careful!
We can't just add 4, 5 and 6 and divide by 3.
There are 20 numbers, not 3.
Each value counts f times.
100 divided by 20 is 5.
4 Check
Let's check: if all 20 numbers were 5, the total would be 5 times 20.
That is 100, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.