Outliers in 4, 5, 6, 6, 7, 8, 20 Step by Step

Step by step

The question

Question: find the outliers in 4, 5, 6, 6, 7, 8 and 20.

4, 5, 6, 6, 7, 8, 20

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: 4, 5, 6, 6, 7, 8 and 20.

= 4, 5, 6, 6, 7, 8, 20

2 Find the quartiles

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

The median is 6.

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: 5.

Q3 is the middle of the upper half: 8.

3 Find the IQR

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

8 minus 5 is 3.

IQR = Q3 − Q1 = 8 − 5 = 3

4 Find the fences

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

1.5 times 3 is 4.5.

1.5 × IQR = 1.5 × 3 = 4.5

The low fence: Q1 minus 4.5.

5 minus 4.5 is 0.5.

low fence = Q1 − 4.5 = 5 − 4.5 = 0.5

The high fence: Q3 plus 4.5.

8 plus 4.5 is 12.5.

high fence = Q3 + 4.5 = 8 + 4.5 = 12.5

5 Find the outliers

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

20 is outside the fences.

So the outlier is 20.

= outlier: 20

6 Check

Let's check each one against its fence.

20 is more than 12.5.

So it is right!

20 > 12.5

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