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Chapter 4: Measures of Position
located an equal distance from the left and right hinges. From these two
observations, we can conclude that the distribution is symmetrical.
(c) Observe that the length of the left whisker = 40 – 5 = 35 and the length
of the right whisker = 65 – 60 = 5. That is, the length of the left whisker is
longer than the length of the right whisker. Also, the median is only
55 – 40 = 15 units from
and 60 – 55 = 5 units from
. That is, the
median is to the right of center in the interquartile box. From these two
observations, we can conclude that the distribution is skewed to the left, or
negatively skewed.
We can use the box plot to display an outlier if it exists.
Outliers Revisited
We can use the box plot to display an outlier if it exists. The outlier is
usually displayed using an appropriate symbol.
Recall the
Inner Fence Test
was used to test whether a data value falls
outside the interval for the inner fences [
– 1.5
,
+ 1.5
].
(Refer to
Section 4-4
).
If a value falls outside this interval, it is usually
denoted by a symbol on the box plot which indicates that is classified as an
outlier.
Example 4-11:
The data given in this example represents the 20 countries
with the largest number of total Summer Olympic medals, including the
United States, which had 101 medals for the 1996 Atlanta Games.
Determine whether the number of medals won by the United States in these
games is an outlier relative to the numbers for the other countries. The data
values are given below.
Data values:
63 65 50 37 35 41 25 23 27 21 17
17 20 19 22 15 15 15 15 101.
Solution
: Using the
Basic Statistics
workbook we can verify that
=
= 17,
=
= 39, and
= 22.
See the results in
Figure 4-24.