Step by step
The question
Question: find the mean of the grouped data with classes 20 to 24, 25 to 29, 30 to 34, 35 to 39 and 40 to 44, and frequencies 6, 9, 7, 4 and 1.
Each class is a range of numbers.
f is how many numbers are in it.
So 6 numbers are from 20 to 24.
1 Find the midpoints
We don't know the numbers themselves.
So each class uses its middle, m: the midpoint.
The middle of 20 and 24: add them, divide by 2.
22.
Next: 27.
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.
22 times 6 is 132.
27 times 9 is 243.
The same for every row.
3 Add the columns
The f column: 27 numbers in all.
The m × f column: 789.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 789 divided by 27.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 5 classes.
There are 27 numbers.
789 divided by 27 is 29.2222.
The books round to one more decimal place than the data.
So the mean is about 29.2.
5 Check
Let's check: 29.2 times 27 is about 789, 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.