Step by step
The question
Question: find the mean of the grouped data with classes 40 to 50, 50 to 60, 60 to 70, 70 to 80 and 80 to 90, and frequencies 3, 7, 12, 6 and 2.
Each class is a range of numbers.
f is how many numbers are in it.
So 3 numbers are from 40 to 50.
1 Find the midpoints
We don't know the numbers themselves.
So each class uses its middle, m: the midpoint.
The middle of 40 and 50: add them, divide by 2.
45.
Next: 55.
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.
45 times 3 is 135.
55 times 7 is 385.
The same for every row.
3 Add the columns
The f column: 30 numbers in all.
The m × f column: 1920.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 1920 divided by 30.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 5 classes.
There are 30 numbers.
1920 divided by 30 is 64.
5 Check
Let's check: 64 times 30 is 1920, 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.