Step by step
The question
Question: find the outliers in 2, 3, 3, 4, 5, 5, 6 and 18.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 2, 3, 3, 4, 5, 5, 6 and 18.
2 Find the quartiles
8 numbers: two in the middle, 4 and 5.
The median goes between them.
It cuts the list in two halves, 4 numbers each.
The median is halfway between them: we add them and divide by 2.
4 plus 5 is 9.
Divided by 2 is 4.5.
The lower half has two in the middle: 3 and 3.
Q1 is halfway between them: we add them and divide by 2.
3 plus 3 is 6.
Divided by 2 is 3.
The upper half has two in the middle: 5 and 6.
Q3 is halfway between them: we add them and divide by 2.
5 plus 6 is 11.
Divided by 2 is 5.5.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
5.5 minus 3 is 2.5.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 2.5 is 3.75.
Careful!
We step out from the ends of the box, Q1 and Q3.
Not from the median.
The low fence: Q1 minus 3.75.
3 minus 3.75 is −0.75.
The high fence: Q3 plus 3.75.
5.5 plus 3.75 is 9.25.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
18 is outside the fences.
So the outlier is 18.
6 Check
Let's check each one against its fence.
18 is more than 9.25.
So it is right!
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.