Boxplots (aka, Box and Whisker Plots)
A boxplot, sometimes called a
box and whisker plot, is a type of graph used
to display patterns of
quantitative data.
Boxplot Basics
A boxplot splits the data set into
quartiles.
The body of the boxplot consists of a "box" (hence, the name),
which goes from the first quartile (Q1) to the third quartile
(Q3).
Within the box, a vertical line is drawn at the Q2, the
median
of the data set. Two horizontal lines, called
whiskers, extend from the front and back of the box.
The front whisker goes from Q1 to the smallest nonoutlier in the data set,
and the back whisker goes from Q3 to the largest nonoutlier.
Smallest nonoutlier 
Q1 
Q2 
Q3 

Largest nonoutlier 






.
.





.
.
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600 
400 
200 
0 
200 
400 
600 
800 
1000 
1200 
1400 
1600 

If the data set includes one or more
outliers, they
are plotted separately as points on the chart. In the boxplot
above, two outliers precede the first whisker; and three outliers follow
the second whisker.
How to Interpret a Boxplot
Here is how to read a boxplot. The median is indicated by the
vertical line that runs down the center of the box. In the boxplot
above, the median is about 400.
Additionally, boxplots display two common measures of the variability
or spread in a data set.

Interquartile range (IQR). The middle half of a data
set falls within the interquartile range. In a boxplot,
the interquartile range is represented by the width of
the box (Q3 minus Q1). In the chart above, the interquartile
range is equal to 600 minus 300 or about 300.
And finally, boxplots often provide information about the shape
of a data set. The examples below show some common
patterns.





Skewed right 

Symmetric 

Skewed left 
Each of the above boxplots illustrates a different
skewness
pattern. If most of the observations are concentrated on
the low end of the scale, the distribution is skewed right;
and vice versa. If a distribution is symmetric, the
observations will be evenly split at the median, as
shown above in the middle figure.
Test Your Understanding of This Lesson
Problem 1
Consider the boxplot below.
Which of the following statements are true?
I. The distribution is skewed right.
II. The interquartile range is about 8.
III. The median is about 10.
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Solution
The correct answer is (B). Most of the observations are on the
high end of the scale, so the distribution is
skewed left.
The
interquartile range is indicated by the length of the
box, which is 18 minus 10 or 8.
And the median is indicated by the vertical line running through
the middle of the box, which is roughly centered over 15. So the
median is about 15.