Mean of the frequency table x: 5, 6, 7, 8; f: 2, 6, 7, 5

Step by step

The question

Question: find the mean of this frequency table.

The values x are 5, 6, 7 and 8.

Their frequencies f are 2, 6, 7 and 5.

x is the value.

f is how many times it comes.

So 5 comes twice.

1 Multiply x × f

A new column: x times f.

It is the total of each row.

5 comes twice: 5 × 2 = 10.

6 comes 6 times: 6 × 6 = 36.

7 comes 7 times: 7 × 7 = 49.

And the same for the last row.

2 Add the columns

We add the f column: 20 numbers in all.

We add the x × f column: the total of all the numbers is 135.

3 Share equally

The mean shares the total equally: 135 divided by 20.

Careful!

We can't just add 5, 6, 7 and 8 and divide by 4.

There are 20 numbers, not 4.

Each value counts f times.

135 divided by 20 is 6.75.

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

So the mean is about 6.8.

4 Check

Let's check: if all 20 numbers were 6.75, the total would be 6.75 times 20.

That is 135, the total.

So it is right!

Let's look back.

First: multiply x × f.

Then: add the columns.

Then: share equally.

Last: check.