Step by step
The question
Question: find the mean of the grouped data with classes 0 to 5, 5 to 10, 10 to 15 and 15 to 20, and frequencies 7, 4, 2 and 1.
Each class is a range of numbers.
f is how many numbers are in it.
So 7 numbers are from 0 to 5.
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 5: add them, divide by 2.
2.5.
Next: 7.5.
Each midpoint is 5 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.
2.5 times 7 is 17.5.
7.5 times 4 is 30.
The same for every row.
3 Add the columns
The f column: 14 numbers in all.
The m × f column: 90.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 90 divided by 14.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 4 classes.
There are 14 numbers.
90 divided by 14 is 6.4286.
The books round to one more decimal place than the data.
So the mean is about 6.4.
5 Check
Let's check: 6.4 times 14 is about 90, 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.