Step by step
The question
Question: find the mean of the grouped data with classes 0 to 1, 1 to 2, 2 to 3 and 3 to 4, and frequencies 5, 8, 4 and 3.
Each class is a range of numbers.
f is how many numbers are in it.
So 5 numbers are from 0 to 1.
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 1: add them, divide by 2.
0.5.
Next: 1.5.
Each midpoint is 1 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.
0.5 times 5 is 2.5.
1.5 times 8 is 12.
The same for every row.
3 Add the columns
The f column: 20 numbers in all.
The m × f column: 35.
That is about the total of all the numbers.
4 Share equally
The mean shares the total equally: 35 divided by 20.
It is only an estimate: the midpoints stand in for the real numbers.
Careful!
Not divided by the 4 classes.
There are 20 numbers.
35 divided by 20 is 1.75.
The books round to one more decimal place than the data.
So the mean is about 1.8.
5 Check
Let's check: 1.8 times 20 is about 35, 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.