Outliers in 3, 20, 21, 22, 23, 24, 25 Step by Step

Step by step

The question

Question: find the outliers in 3, 20, 21, 22, 23, 24 and 25.

3, 20, 21, 22, 23, 24, 25

An outlier is a number far away from the others.

outlier: far from the others

1 Put them in order

First we put them in order, smallest first: 3, 20, 21, 22, 23, 24 and 25.

= 3, 20, 21, 22, 23, 24, 25

2 Find the quartiles

7 numbers: 3 on each side of the middle one.

The median is 22.

The median cuts the list in two halves, 3 numbers each.

The median itself is in neither half.

Careful!

The median is not counted in the halves.

Each half has 3 numbers.

Careful: the median is in neither half

Q1 is the middle of the lower half: 20.

Q3 is the middle of the upper half: 24.

3 Find the IQR

The IQR is Q3 minus Q1: how wide the middle half is.

24 minus 20 is 4.

IQR = Q3 − Q1 = 24 − 20 = 4

4 Find the fences

The rule: an outlier is more than 1.5 IQRs outside the box.

1.5 times 4 is 6.

1.5 × IQR = 1.5 × 4 = 6

The low fence: Q1 minus 6.

20 minus 6 is 14.

low fence = Q1 − 6 = 20 − 6 = 14

The high fence: Q3 plus 6.

24 plus 6 is 30.

high fence = Q3 + 6 = 24 + 6 = 30

5 Find the outliers

On a number line: the fences in red, and a dot for each number.

3 is outside the fences.

So the outlier is 3.

= outlier: 3

6 Check

Let's check each one against its fence.

3 is less than 14.

So it is right!

3 < 14

Let's look back.

First: put them in order.

Then: find the quartiles.

Then: find the IQR.

Then: find the fences.

Then: find the outliers.

Last: check.

Answer