Mean of grouped data 0-2: 6, 2-4: 9, 4-6: 5 Step by Step

Step by step

The question

Question: find the mean of the grouped data with classes 0 to 2, 2 to 4 and 4 to 6, and frequencies 6, 9 and 5.

Mean of the grouped data

Each class is a range of numbers.

f is how many numbers are in it.

So 6 numbers are from 0 to 2.

f = how many, m = the middle of the class

1 Find the midpoints

We don't know the numbers themselves.

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

m = (0 + 2) ÷ 2 = 1

The middle of 0 and 2: add them, divide by 2.

Next: 3.

Each midpoint is 2 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.

1 times 6 is 6.

3 times 9 is 27.

The same for every row.

3 Add the columns

The f column: 20 numbers in all.

6 + 9 + 5 = 20

The m × f column: 58.

That is about the total of all the numbers.

6 + 27 + 25 = 58

4 Share equally

The mean shares the total equally: 58 divided by 20.

mean ≈ 5820

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

≈ : an estimate, from the midpoints

Careful!

Not divided by the 3 classes.

There are 20 numbers.

Careful: not 583 ✗

58 divided by 20 is 2.9.

mean ≈ 2.9

5 Check

Let's check: 2.9 times 20 is 58, the total.

2.9 × 20 = 58

And the mean is between the first and the last midpoints.

So it makes sense!

1 < 2.9 < 5

Let's look back.

First: find the midpoints.

Then: multiply m × f.

Then: add the columns.

Then: share equally.

Last: check.

Answer