Step by step
The question
Question: find the mean of the grouped data with classes 10 to 19, 20 to 29, 30 to 39, 40 to 49 and 50 to 59, and frequencies 2, 5, 8, 4 and 1.
Each class is a range of numbers.
f is how many numbers are in it.
So 2 numbers are from 10 to 19.
1 Find the midpoints
We don't know the numbers themselves.
So each class uses its middle, m: the midpoint.
The middle of 10 and 19: add them, divide by 2.
14.5.
Next: 24.5.
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.
14.5 times 2 is 29.
24.5 times 5 is 122.5.
The same for every row.
3 Add the columns
The f column: 20 numbers in all.
The m × f column: 660.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 660 divided by 20.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 5 classes.
There are 20 numbers.
660 divided by 20 is 33.
5 Check
Let's check: 33 times 20 is 660, 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.