Step by step
The question
Question: find the mean of this frequency table.
The values x are 2, 4 and 6.
Their frequencies f are 1, 2 and 1.
x is the value.
f is how many times it comes.
So 2 comes once.
1 Multiply x × f
A new column: x times f.
It is the total of each row.
2 comes once: 2 × 1 = 2.
4 comes twice: 4 × 2 = 8.
6 comes once: 6 × 1 = 6.
2 Add the columns
We add the f column: 4 numbers in all.
We add the x × f column: the total of all the numbers is 16.
3 Share equally
The mean shares the total equally: 16 divided by 4.
Careful!
We can't just add 2, 4 and 6 and divide by 3.
There are 4 numbers, not 3.
Each value counts f times.
16 divided by 4 is 4.
4 Check
Let's check: if all 4 numbers were 4, the total would be 4 times 4.
That is 16, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.