Step by step
The question
Question: find the outliers in 8, 9, 10, 10, 11, 12, 13 and 2.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 2, 8, 9, 10, 10, 11, 12 and 13.
2 Find the quartiles
8 numbers: two in the middle, 10 and 10.
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.
10 plus 10 is 20.
Divided by 2 is 10.
The lower half has two in the middle: 8 and 9.
Q1 is halfway between them: we add them and divide by 2.
8 plus 9 is 17.
Divided by 2 is 8.5.
The upper half has two in the middle: 11 and 12.
Q3 is halfway between them: we add them and divide by 2.
11 plus 12 is 23.
Divided by 2 is 11.5.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
11.5 minus 8.5 is 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.
Careful!
We step out from the ends of the box, Q1 and Q3.
Not from the median.
The low fence: Q1 minus 4.5.
8.5 minus 4.5 is 4.
The high fence: Q3 plus 4.5.
11.5 plus 4.5 is 16.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
2 is outside the fences.
So the outlier is 2.
6 Check
Let's check each one against its fence.
2 is less than 4.
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.