Step by step
The question
Question: find the mean of the grouped data with classes 0 to 10, 10 to 20, 20 to 30 and 30 to 40, and frequencies 5, 9, 4 and 2.
Each class is a range of numbers.
f is how many numbers are in it.
So 5 numbers are from 0 to 10.
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 10: add them, divide by 2.
5.
Next: 15.
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.
5 times 5 is 25.
15 times 9 is 135.
The same for every row.
3 Add the columns
The f column: 20 numbers in all.
The m × f column: 330.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 330 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.
330 divided by 20 is 16.5.
5 Check
Let's check: 16.5 times 20 is 330, 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.