Step by step
The question
Question: find the mean of this frequency table.
The values x are 2, 3, 4, 5 and 6.
Their frequencies f are 1, 4, 6, 5 and 4.
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.
3 comes 4 times: 3 × 4 = 12.
4 comes 6 times: 4 × 6 = 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 87.
3 Share equally
The mean shares the total equally: 87 divided by 20.
Careful!
We can't just add 2, 3, 4, 5 and 6 and divide by 5.
There are 20 numbers, not 5.
Each value counts f times.
87 divided by 20 is 4.35.
The books round to one more decimal place than the data.
So the mean is about 4.4.
4 Check
Let's check: if all 20 numbers were 4.35, the total would be 4.35 times 20.
That is 87, the total.
So it is right!
Let's look back.
First: multiply x × f.
Then: add the columns.
Then: share equally.
Last: check.