Mean of the frequency table x: 1.5, 2.5, 3.5; f: 2, 5, 3

Step by step

The question

Question: find the mean of this frequency table.

The values x are 1.5, 2.5 and 3.5.

Their frequencies f are 2, 5 and 3.

x is the value.

f is how many times it comes.

So 1.5 comes twice.

1 Multiply x × f

A new column: x times f.

It is the total of each row.

1.5 comes twice: 1.5 × 2 = 3.

2.5 comes 5 times: 2.5 × 5 = 12.5.

3.5 comes 3 times: 3.5 × 3 = 10.5.

2 Add the columns

We add the f column: 10 numbers in all.

We add the x × f column: the total of all the numbers is 26.

3 Share equally

The mean shares the total equally: 26 divided by 10.

Careful!

We can't just add 1.5, 2.5 and 3.5 and divide by 3.

There are 10 numbers, not 3.

Each value counts f times.

26 divided by 10 is 2.6.

4 Check

Let's check: if all 10 numbers were 2.6, the total would be 2.6 times 10.

That is 26, the total.

So it is right!

Let's look back.

First: multiply x × f.

Then: add the columns.

Then: share equally.

Last: check.