Step by step
The question
Question: find the mean of the grouped data with classes 0 to 30, 30 to 60, 60 to 90 and 90 to 120, and frequencies 4, 11, 8 and 3.
Each class is a range of numbers.
f is how many numbers are in it.
So 4 numbers are from 0 to 30.
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 30: add them, divide by 2.
15.
Next: 45.
Each midpoint is 30 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.
15 times 4 is 60.
45 times 11 is 495.
The same for every row.
3 Add the columns
The f column: 26 numbers in all.
The m × f column: 1470.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 1470 divided by 26.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 4 classes.
There are 26 numbers.
1470 divided by 26 is 56.5385.
The books round to one more decimal place than the data.
So the mean is about 56.5.
5 Check
Let's check: 56.5 times 26 is about 1470, 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.