Mean of grouped data 60-69: 2, 70-79: 6, 80-89: 9, 90-99: 4

Step by step

The question

Question: find the mean of the grouped data with classes 60 to 69, 70 to 79, 80 to 89 and 90 to 99, and frequencies 2, 6, 9 and 4.

Each class is a range of numbers.

f is how many numbers are in it.

So 2 numbers are from 60 to 69.

1 Find the midpoints

We don't know the numbers themselves.

So each class uses its middle, m: the midpoint.

The middle of 60 and 69: add them, divide by 2.

64.5.

Next: 74.5.

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.

64.5 times 2 is 129.

74.5 times 6 is 447.

The same for every row.

3 Add the columns

The f column: 21 numbers in all.

The m × f column: 1714.5.

That is about the total of all the numbers.

4 Share equally

The mean shares the total equally: 1714.5 divided by 21.

It is only an estimate: the midpoints stand in for the real numbers.

Careful!

Not divided by the 4 classes.

There are 21 numbers.

1714.5 divided by 21 is 81.6429.

The books round to one more decimal place than the data.

So the mean is about 81.6.

5 Check

Let's check: 81.6 times 21 is about 1714.5, 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.