Step by step
The question
Question: find the mean of the grouped data with classes 100 to 120, 120 to 140, 140 to 160 and 160 to 180, and frequencies 4, 9, 5 and 2.
Each class is a range of numbers.
f is how many numbers are in it.
So 4 numbers are from 100 to 120.
1 Find the midpoints
We don't know the numbers themselves.
So each class uses its middle, m: the midpoint.
The middle of 100 and 120: add them, divide by 2.
110.
Next: 130.
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.
110 times 4 is 440.
130 times 9 is 1170.
The same for every row.
3 Add the columns
The f column: 20 numbers in all.
The m × f column: 2700.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 2700 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.
2700 divided by 20 is 135.
5 Check
Let's check: 135 times 20 is 2700, 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.