Step by step
The question
Question: find the outliers in 50, 52, 55, 56, 58, 60, 61 and 95.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 50, 52, 55, 56, 58, 60, 61 and 95.
2 Find the quartiles
8 numbers: two in the middle, 56 and 58.
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.
56 plus 58 is 114.
Divided by 2 is 57.
The lower half has two in the middle: 52 and 55.
Q1 is halfway between them: we add them and divide by 2.
52 plus 55 is 107.
Divided by 2 is 53.5.
The upper half has two in the middle: 60 and 61.
Q3 is halfway between them: we add them and divide by 2.
60 plus 61 is 121.
Divided by 2 is 60.5.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
60.5 minus 53.5 is 7.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 7 is 10.5.
Careful!
We step out from the ends of the box, Q1 and Q3.
Not from the median.
The low fence: Q1 minus 10.5.
53.5 minus 10.5 is 43.
The high fence: Q3 plus 10.5.
60.5 plus 10.5 is 71.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
95 is outside the fences.
So the outlier is 95.
6 Check
Let's check each one against its fence.
95 is more than 71.
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.