Step by step
The question
Question: find the mean of this frequency table.
The values x are 1, 2, 3, 4 and 5.
Their frequencies f are 2, 5, 9, 6 and 3.
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 5 times: 2 × 5 = 10.
3 comes 9 times: 3 × 9 = 27.
And the same for the last row.
2 Add the columns
We add the f column: 25 numbers in all.
We add the x × f column: the total of all the numbers is 78.
3 Share equally
The mean shares the total equally: 78 divided by 25.
Careful!
We can't just add 1, 2, 3, 4 and 5 and divide by 5.
There are 25 numbers, not 5.
Each value counts f times.
78 divided by 25 is 3.12.
The books round to one more decimal place than the data.
So the mean is about 3.1.
4 Check
Let's check: if all 25 numbers were 3.12, the total would be 3.12 times 25.
That is 78, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.