Step by step
The question
Question: find the mean of the grouped data with classes 0 to 9, 10 to 19, 20 to 29 and 30 to 39, and frequencies 4, 7, 6 and 3.
Each class is a range of numbers.
f is how many numbers are in it.
So 4 numbers are from 0 to 9.
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 9: add them, divide by 2.
4.5.
Next: 14.5.
Each midpoint is 10 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.
4.5 times 4 is 18.
14.5 times 7 is 101.5.
The same for every row.
3 Add the columns
The f column: 20 numbers in all.
The m × f column: 370.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 370 divided by 20.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 4 classes.
There are 20 numbers.
370 divided by 20 is 18.5.
5 Check
Let's check: 18.5 times 20 is 370, 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.