Step by step
The question
Question: find the outliers in 40, 42, 45, 47, 48, 50, 53, 55, 90 and 5.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 5, 40, 42, 45, 47, 48, 50, 53, 55 and 90.
2 Find the quartiles
10 numbers: two in the middle, 47 and 48.
The median goes between them.
It cuts the list in two halves, 5 numbers each.
The median is halfway between them: we add them and divide by 2.
47 plus 48 is 95.
Divided by 2 is 47.5.
Q1 is the middle of the lower half: 42.
Q3 is the middle of the upper half: 53.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
53 minus 42 is 11.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 11 is 16.5.
Careful!
We step out from the ends of the box, Q1 and Q3.
Not from the median.
The low fence: Q1 minus 16.5.
42 minus 16.5 is 25.5.
The high fence: Q3 plus 16.5.
53 plus 16.5 is 69.5.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
5 and 90 are outside the fences.
So the outliers are 5 and 90.
6 Check
Let's check each one against its fence.
5 is less than 25.5.
90 is more than 69.5.
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.