Step by step
The question
Question: find the mean of the grouped data with classes 0 to 6, 6 to 12, 12 to 18 and 18 to 24, and frequencies 1, 4, 3 and 2.
Each class is a range of numbers.
f is how many numbers are in it.
So 1 numbers are from 0 to 6.
1 Find the midpoints
We don't know the numbers themselves.
So each class uses its middle, m: the midpoint.
The middle of 0 and 6: add them, divide by 2.
3.
Next: 9.
Each midpoint is 6 more.
And so on.
2 Multiply m × f
Each number in a class counts as its midpoint.
So a class adds up to m times f.
3 times 1 is 3.
9 times 4 is 36.
The same for every row.
3 Add the columns
The f column: 10 numbers in all.
The m × f column: 126.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 126 divided by 10.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 4 classes.
There are 10 numbers.
126 divided by 10 is 12.6.
5 Check
Let's check: 12.6 times 10 is 126, the total.
And the mean is between the first and the last midpoints.
So it makes sense!
Let's look back.
First: find the midpoints.
Then: multiply m × f.
Then: add the columns.
Then: share equally.
Last: check.