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Chapter 3: Measures of Variability
119
Solution
: Based on the above discussion relating to the standard deviation,
the result will be 5.14 (to two decimal places) as shown below.
√
Note that both the values for the sample variance and standard deviation are
displayed in
Figure 3-14
.
Notes:
If all of the observations have the same value, the sample variance
(standard deviation) will be zero. That is, there is no variability in the
data set.
The variance (standard deviation) is influenced by outliers in the data
set.
The unit for the standard deviation is the same as that for the raw data.
Thus, it is preferred to use the standard deviation rather than the
variance as the measure of variability.
To emphasize, the characteristic of the standard deviation having the same
unit as the variable is a very important one. Because of this, the standard
deviation is a much more useful measure than the variance, which is in
square units.
Example 3-10:
What is the variance and standard deviation for the
following sample values?
3, 3, 3, 3, 3, 3
Note:
The values in this data set are all the same.
Solution:
Using the
Basic Statistics
workbook, observe the value of the
sample variance (as well as the standard deviation) is 0. That is, there is no
variability in a data set whose values are all the same. The results, shown in
Figure 3-15
, support the first bulleted point in the previous notes box.