Step by step
The question
Question: find the mean of this frequency table.
The values x are 1, 2, 3 and 4.
Their frequencies f are 3, 5, 8 and 4.
x is the value.
f is how many times it comes.
So 1 comes 3 times.
1 Multiply x × f
A new column: x times f.
It is the total of each row.
1 comes 3 times: 1 × 3 = 3.
2 comes 5 times: 2 × 5 = 10.
3 comes 8 times: 3 × 8 = 24.
And the same for the last row.
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 53.
3 Share equally
The mean shares the total equally: 53 divided by 20.
Careful!
We can't just add 1, 2, 3 and 4 and divide by 4.
There are 20 numbers, not 4.
Each value counts f times.
53 divided by 20 is 2.65.
The books round to one more decimal place than the data.
So the mean is about 2.7.
4 Check
Let's check: if all 20 numbers were 2.65, the total would be 2.65 times 20.
That is 53, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.