Step by step
The question
Question: find the mean of this frequency table.
The values x are 0, 1, 2 and 3.
Their frequencies f are 7, 9, 5 and 3.
x is the value.
f is how many times it comes.
So 0 comes 7 times.
1 Multiply x × f
A new column: x times f.
It is the total of each row.
0 comes 7 times: 0 × 7 = 0.
1 comes 9 times: 1 × 9 = 9.
2 comes 5 times: 2 × 5 = 10.
And the same for the last row.
2 Add the columns
We add the f column: 24 numbers in all.
We add the x × f column: the total of all the numbers is 28.
3 Share equally
The mean shares the total equally: 28 divided by 24.
Careful!
We can't just add 0, 1, 2 and 3 and divide by 4.
There are 24 numbers, not 4.
Each value counts f times.
28 divided by 24 is 1.1667.
The books round to one more decimal place than the data.
So the mean is about 1.2.
4 Check
Let's check: if all 24 numbers were 1.1667, the total would be 1.1667 times 24.
That is 28, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.