Step by step
The question
Question: find the mean of the grouped data with classes 15 to 25, 25 to 35, 35 to 45, 45 to 55 and 55 to 65, and frequencies 3, 5, 8, 6 and 2.
Each class is a range of numbers.
f is how many numbers are in it.
So 3 numbers are from 15 to 25.
1 Find the midpoints
We don't know the numbers themselves.
So each class uses its middle, m: the midpoint.
The middle of 15 and 25: add them, divide by 2.
20.
Next: 30.
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.
20 times 3 is 60.
30 times 5 is 150.
The same for every row.
3 Add the columns
The f column: 24 numbers in all.
The m × f column: 950.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 950 divided by 24.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 5 classes.
There are 24 numbers.
950 divided by 24 is 39.5833.
The books round to one more decimal place than the data.
So the mean is about 39.6.
5 Check
Let's check: 39.6 times 24 is about 950, 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.