Step by step
The question
Question: find the mean of the grouped data with classes 0 to 20, 20 to 40 and 40 to 60, and frequencies 4, 10 and 6.
Each class is a range of numbers.
f is how many numbers are in it.
So 4 numbers are from 0 to 20.
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 20: add them, divide by 2.
10.
Next: 30.
Each midpoint is 20 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.
10 times 4 is 40.
30 times 10 is 300.
The same for every row.
3 Add the columns
The f column: 20 numbers in all.
The m × f column: 640.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 640 divided by 20.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 3 classes.
There are 20 numbers.
640 divided by 20 is 32.
5 Check
Let's check: 32 times 20 is 640, 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.