- Compute Q1, Q2 and Q3. Also, compute the interquartile range
IQR = Q3 - Q1.
Example: Suppose that the
dataset consists of these hypothetical test scores:
5 39 75 79 85 90
91 93 93 98
Q1 = 75, Q2 = 88, Q3 = 92. IQR = 93 - 75 = 18.
- Draw three horizontal lines, all of the same length and
all starting at the same x-value:
one at height Q1, the second at Q2 and
the third at Q3.
Example: Here is the
boxplot after Step 2.
- Draw two vertical lines, one at connecting the left endpoints
of the lines and the other connecting their right endpoints.
Example: Here is the
updated boxplot after Step 3.
- Compute the inner fences IF1 = Q1 - 1.5 * IQR and
IF2 = Q3 + 1.5 * IQR.
Example: The inner fences are
IF1 = 75 - 1.5 * 18 = 42 and IF2 = 92 + 1.5 * 18 = 110.
- Draw a whisker downward from Q1 to IF1 or Q0, whichever comes first.
Draw a whisker upward from Q3 to IF2 or Q4, whichever comes first.
Example: Here is the
boxplot after adding the whiskers in Step 4.
- Compute the outer fences OF1 = Q1 - 3 * IQR and OF2 = Q3 + 3 * IQR.
Example: The outer fences are
OF1 = 75 - 3 * 18 = 21 and OF2 = 92 + 3 * 18 = 146.
- Extreme outliers are observations that are beyond one of the
outer fences OF1 or OF2. Mark any extreme outliers on the boxplot
with an asterisk (*).
Example: The only observation less than
OF1 = 21 is 5. Here is the
boxplot after marking 5 with a *.
- Mild outliers are observations that are between an inner and
outer fence. Mild outliers are marked with a circle (O).
Example: The only observation that is
between an inner fence and an outer fence is 39, which is between
IF1 = 42 and OF1 = 21. Here is the
boxplot after marking 39 with a O.