Step by step
The question
Question: find the outliers in 25, 28, 30, 31, 33, 34, 36, 38, 39 and 41.
An outlier is a number far away from the others.
1 Put them in order
First we put them in order, smallest first: 25, 28, 30, 31, 33, 34, 36, 38, 39 and 41.
2 Find the quartiles
10 numbers: two in the middle, 33 and 34.
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.
33 plus 34 is 67.
Divided by 2 is 33.5.
Q1 is the middle of the lower half: 30.
Q3 is the middle of the upper half: 38.
3 Find the IQR
The IQR is Q3 minus Q1: how wide the middle half is.
38 minus 30 is 8.
4 Find the fences
The rule: an outlier is more than 1.5 IQRs outside the box.
1.5 times 8 is 12.
Careful!
We step out from the ends of the box, Q1 and Q3.
Not from the median.
The low fence: Q1 minus 12.
30 minus 12 is 18.
The high fence: Q3 plus 12.
38 plus 12 is 50.
5 Find the outliers
On a number line: the fences in red, and a dot for each number.
Every dot is between the fences.
No number is outside the fences.
So there are no outliers.
6 Check
Let's check the ends: 25 is above 18, and 41 is below 50.
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.