Mean of the frequency table x: 0, 1, 2; f: 6, 3, 1 Step by Step

Step by step

The question

Question: find the mean of this frequency table.

The values x are 0, 1 and 2.

Their frequencies f are 6, 3 and 1.

Mean of the frequency table

x is the value.

f is how many times it comes.

So 0 comes 6 times.

f = how many times

1 Multiply x × f

A new column: x times f.

It is the total of each row.

0 comes 6 times: 0 × 6 = 0.

1 comes 3 times: 1 × 3 = 3.

2 comes once: 2 × 1 = 2.

2 Add the columns

We add the f column: 10 numbers in all.

6 + 3 + 1 = 10

We add the x × f column: the total of all the numbers is 5.

0 + 3 + 2 = 5

3 Share equally

The mean shares the total equally: 5 divided by 10.

mean = 510

Careful!

We can't just add 0, 1 and 2 and divide by 3.

There are 10 numbers, not 3.

Each value counts f times.

Careful: not 0 + 1 + 23 ✗

5 divided by 10 is 0.5.

mean = 0.5

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

So the mean is about 0.5.

mean ≈ 0.5

1 decimal place: 1 more than the data

4 Check

Let's check: if all 10 numbers were 0.5, the total would be 0.5 times 10.

That is 5, the total.

So it is right!

0.5 × 10 = 5

Let's look back.

First: multiply x × f.

Then: add the columns.

Then: share equally.

Last: check.

Answer