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Chapter 18: A. Basic Statistics and Applications 233
Construction of a Box Plot
Step 1. For a given data set first find the quartiles Q 1 , Q 2 , and Q 3 .
Step 2. Draw a box with its outer lines standing at the first quartile (Q 1 )
and the third quartile (Q 3 ) and then draw a line at the second
quartile (Q 2 ). The line at Q 2 divides the box into two boxes, which
may or may not be of equal size.
Step 3. From the center of the outer lines draw straight lines extending
outwardly up to three times the interquartile range (IQR) and
mark them as shown in Figure 18.21. Note that each distance
between the points A and B, B and C, D and E, and E and F is
equal to one and one-half times the distance between the points
A and D, or one and one-half times the interquartile range (IQR).
The points S and L are respectively the smallest and largest data
points that fall within the inner fences. The lines from A to S and
D to L are called the whiskers.
How to Use the Box Plot. About the outliers:
1. Any data points that fall beyond the lower and upper outer fences
are the extreme outliers. These points are usually excluded from
the analysis.
2. Any data points between the inner and outer fences are the mild
outliers. These points are excluded from the analysis only if we
are convinced that these points are in error.
About the shape of the distribution:
1. If the second quartile (median) is close to the center of the box and
each of the whiskers is approximately of equal length, then the
distribution is symmetric.
2. If the right box is substantially larger that the left box and/or the right
whisker is much longer than the left whisker then the distribution is
right-skewed.
3. If the left box is substantially larger than the right box and/or the left
whisker is much longer than the right whisker than the distribution is
left-skewed.
Part IV.A.4
EXAMPLE 18.24
The following data give the noise level measured in decibels (a normal conversation by
humans produces noise level of about 75 decibels) produced by different machines in
a very large manufacturing plant.
85, 80, 88, 95, 115, 110, 105, 104, 89, 87, 96, 140, 75, 79, 99
Construct a box plot and determine whether the data set contains any outliers.
Continued