how can you tell is a box plot contains outliers

Question

How do you know if a box plot contains outliers?

Answer 1

I'll use a random set of data as an example:

 

1, 7, 11, 9, 8, 7, 9, 6, 8

 

 

 

STEP 1: PUT THE DATA IN ORDER FROM LEAST TO GREATEST

 

1, 6, 7, 7, 8, 8, 9, 9, 11

 

 

 

STEP 2: FIND THE MEDIAN (MIDDLE NUMBER)

 

Since there are 9 values in my data set (an odd number), the median is the (9+1)/2 = 10/2 = 5th value:

 

1, 6, 7, 7, 8, 8, 9, 9, 11

 

The median, also called Q2 (Quartile 2), divides the set of data in half. The lower half is 1, 6, 7, 7 and the upper half is 8, 9, 9, 11.

 

 

 

STEP 3: FIND QUARTILE 1 (Q1, THE MEDIAN OF THE LOWER HALF)

 

Since there are 4 values in the lower half, there's no middle number. That means Q1 is the average of the two middle numbers:

 

1, 6, 7, 7

 

Q1 = (6+7)/2 = 13/2 = 6.5

 

 

 

STEP 4: FIND QUARTILE 3 (Q3, THE MEDIAN OF THE UPPER HALF)

 

Since there are 4 values in the upper half, there's no middle number. That means Quartile 3 (Q3) is the average of the two middle numbers:

 

8, 9, 9, 11

 

Q3 = (9+9)/2 = 18/2 = 9

 

(Note that, since the two middle numbers are the same, Q3 is just equal to that value.)

 

 

 

STEP 5: COMPUTE THE INTERQUARTILE RANGE (IQR)

 

Finding the Interquartile Range (IQR) is like finding the Range of a set of data, but this time, instead of subtracting the lowest value from the highest (our Range is 11 - 1 = 10), we subtract Q1 from Q3:

 

IQR = Q3 - Q1 = 9 - 6.5 = 2.5

 

 

 

STEP 6: TEST FOR OUTLIERS

 

We'll use Q1 and the IQR to test for outliers on the low end and Q3 and the IQR to test for outliers on the high end. Basically, for the low end, we'll find a value that's far enough below Q1 that anything less than it is an outlier. For the high end, we'll find a value that's far enough above Q3 that anything greater than it is an outlier.

 

The low end equation is:

 

Q1 - 1.5(IQR) = 6.5 - (1.5)(2.5) = 6.5 - 3.75 = 2.75

 

So, anything less than 2.75 is an outlier. We do have a value less than 2.75: 1 is an outlier.

 

The high end equation is:

 

Q3 + 1.5(IQR) = 9 + (1.5)(2.5) = 9 + 3.75 = 12.75

 

So, anything greater than 12.75 is an outlier. We don't have any values greater than 12.75.

 

 

This means that there is only one outlier in my data set: 1. 

 

 

Hope this helps!