Step by step
The question
Question: find the outliers in 7, 21, 23, 24, 25, 27, 28, 29, 31 and 50.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 7, 21, 23, 24, 25, 27, 28, 29, 31 and 50.
2 Find the quartiles
10 numbers: two in the middle, 25 and 27.
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.
25 plus 27 is 52.
Divided by 2 is 26.
Q1 is the middle of the lower half: 23.
Q3 is the middle of the upper half: 29.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
29 minus 23 is 6.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 6 is 9.
Careful!
We step out from the ends of the box, Q1 and Q3.
Not from the median.
The low fence: Q1 minus 9.
23 minus 9 is 14.
The high fence: Q3 plus 9.
29 plus 9 is 38.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
7 and 50 are outside the fences.
So the outliers are 7 and 50.
6 Check
Let's check each one against its fence.
7 is less than 14.
50 is more than 38.
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.