Step by step
The question
Question: find the outliers in 100, 104, 106, 108, 110, 111, 113, 150 and 60.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 60, 100, 104, 106, 108, 110, 111, 113 and 150.
2 Find the quartiles
9 numbers: 4 on each side of the middle one.
The median is 108.
The median cuts the list in two halves, 4 numbers each.
The median itself is in neither half.
Careful!
The median is not counted in the halves.
Each half has 4 numbers.
The lower half has two in the middle: 100 and 104.
Q1 is halfway between them: we add them and divide by 2.
100 plus 104 is 204.
Divided by 2 is 102.
The upper half has two in the middle: 111 and 113.
Q3 is halfway between them: we add them and divide by 2.
111 plus 113 is 224.
Divided by 2 is 112.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
112 minus 102 is 10.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 10 is 15.
The low fence: Q1 minus 15.
102 minus 15 is 87.
The high fence: Q3 plus 15.
112 plus 15 is 127.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
60 and 150 are outside the fences.
So the outliers are 60 and 150.
6 Check
Let's check each one against its fence.
60 is less than 87.
150 is more than 127.
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.