Step by step
The question
Question: find the mean of this frequency table.
The values x are 10, 20 and 30.
Their frequencies f are 3, 4 and 3.
x is the value.
f is how many times it comes.
So 10 comes 3 times.
1 Multiply x × f
A new column: x times f.
It is the total of each row.
10 comes 3 times: 10 × 3 = 30.
20 comes 4 times: 20 × 4 = 80.
30 comes 3 times: 30 × 3 = 90.
2 Add the columns
We add the f column: 10 numbers in all.
We add the x × f column: the total of all the numbers is 200.
3 Share equally
The mean shares the total equally: 200 divided by 10.
Careful!
We can't just add 10, 20 and 30 and divide by 3.
There are 10 numbers, not 3.
Each value counts f times.
200 divided by 10 is 20.
4 Check
Let's check: if all 10 numbers were 20, the total would be 20 times 10.
That is 200, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.