Mean of grouped data 0-10: 3, 10-20: 7, 20-30: 6, 30-40: 4

Step by step

The question

Question: find the mean of the grouped data with classes 0 to 10, 10 to 20, 20 to 30 and 30 to 40, and frequencies 3, 7, 6 and 4.

Each class is a range of numbers.

f is how many numbers are in it.

So 3 numbers are from 0 to 10.

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 10: add them, divide by 2.

5.

Next: 15.

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.

5 times 3 is 15.

15 times 7 is 105.

The same for every row.

3 Add the columns

The f column: 20 numbers in all.

The m × f column: 410.

That is about the total of all the numbers.

4 Share equally

The mean shares the total equally: 410 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.

410 divided by 20 is 20.5.

5 Check

Let's check: 20.5 times 20 is 410, 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.