How do you find the outlier number?

Answer 1

Find the inter quartile range, which is IQR = Q3 - Q1, where Q3 is the third quartile and Q1 is the first quartile. Then find these two numbers:

a) Q1 - 1.5*IQR

b) Q3 + 1.5*IQR

Any observation that is below a) or above b) can be considered an outlier.

Chadwick, quartiles are considered robust, meaning that they are not highly effected by outliers. This is because it takes location into account, not the values. Let's look at your data set (sorted).

2 3 6 9 13 18 21 106

position of Q1 = (8+1)/4 = 2.25

Q1 = 0.75(3)+0.25(6) = 3.75

position of Q2 = (8+1)/2 = 4.5

Q2 = (9+13)/2 = 11

position of Q3 = 3(8+1)/4 = 6.75

Q3 = 0.25(18)+0.75(21) = 20.25

Notice that none of these actually use the value 106. Let's continue.

So IQR = Q3-Q1 = 20.25-3.75 = 16.5

Q1-1.5*IQR = 3.75-1.5*16.5 = -21

Q3+1.5*IQR = 20.25+1.5*16.5 = 45

No numbers are below -21, but 106 is above 45, so it can be considered an outlier.