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Chapter 4: Measures of Position
165
4-4 Outliers
In earlier chapters, we implied that a given data value may be considered as
an outlier if it is an extremely small or extremely large data value when
compared with the rest of the data values. Here we will introduce a
procedure which one can use to check to determine whether a value in a data
set can be classified as an outlier.
The following procedure is one of several which allow us to check whether a
data value can be considered as an outlier. It will be referred to as the
Inner
Fence Test.
Procedure to Check for Outliers – Inner Fence Test
The following steps will allow us to use the
Inner Fence Test
to check
whether a given value in a data set can be classified as an outlier.
Step 1
:
Arrange the data in order from the minimum value to maximum
value.
Step 2:
Determine the first quartile
and the third quartile
. Recall that
=
and
=
.
Step 3:
Determine the interquartile range (
) by computing
–
.
Step 4:
Compute
– 1.5
and
+ 1.5
. These endpoints are
called the
lower
and
upper inner fence
respectively.
Step 5:
Let
be the data value that is being checked to determine whether it
is an outlier.
(a)
If the value of
is smaller than the lower inner fence
(
– 1.5
), then
is classified as an outlier.
(b) If the value of
is greater than the upper inner fence
(
+ 1.5
), then
x
is classified as an outlier.