Step by step
The question
Question: find the mean of this frequency table.
The values x are 1, 2 and 3.
Their frequencies f are 2, 3 and 5.
x is the value.
f is how many times it comes.
So 1 comes twice.
1 Multiply x × f
A new column: x times f.
It is the total of each row.
1 comes twice: 1 × 2 = 2.
2 comes 3 times: 2 × 3 = 6.
3 comes 5 times: 3 × 5 = 15.
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 23.
3 Share equally
The mean shares the total equally: 23 divided by 10.
Careful!
We can't just add 1, 2 and 3 and divide by 3.
There are 10 numbers, not 3.
Each value counts f times.
23 divided by 10 is 2.3.
The books round to one more decimal place than the data.
So the mean is about 2.3.
4 Check
Let's check: if all 10 numbers were 2.3, the total would be 2.3 times 10.
That is 23, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.