Step by step
The question
Question: find the outliers in 10, 12, 13, 14, 15, 16 and 40.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 10, 12, 13, 14, 15, 16 and 40.
2 Find the quartiles
7 numbers: 3 on each side of the middle one.
The median is 14.
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.
Q1 is the middle of the lower half: 12.
Q3 is the middle of the upper half: 16.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
16 minus 12 is 4.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 4 is 6.
The low fence: Q1 minus 6.
12 minus 6 is 6.
The high fence: Q3 plus 6.
16 plus 6 is 22.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
40 is outside the fences.
So the outlier is 40.
6 Check
Let's check each one against its fence.
40 is more than 22.
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.