Step by step
The question
Question: find the mean of the grouped data with classes 0 to 4, 4 to 8 and 8 to 12, and frequencies 2, 5 and 3.
Each class is a range of numbers.
f is how many numbers are in it.
So 2 numbers are from 0 to 4.
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 4: add them, divide by 2.
2.
Next: 6.
Each midpoint is 4 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.
2 times 2 is 4.
6 times 5 is 30.
The same for every row.
3 Add the columns
The f column: 10 numbers in all.
The m × f column: 64.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 64 divided by 10.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 3 classes.
There are 10 numbers.
64 divided by 10 is 6.4.
5 Check
Let's check: 6.4 times 10 is 64, 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.