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Chapter 4: Measures of Position
The value of a
-score can be either positive, negative or zero. The
-score
will be zero when the data value
x
is equal to the sample or the population
mean.
Note:
The
-score is the number of standard deviations the data value falls above
(positive
-score) or below (negative
z
-score) the mean for the data set.
Since
-scores are computed for numerical values, then these
-score values
can be affected if there are outliers in the data set.
Note:
The
-score is affected by an outlying value in the data set, since the outlier
(very small or very large value relative to the size of the other values in the
data set) directly affects the value of the mean and the standard deviation.
Example 4-1:
What is the
z-
score for the value of 18 in the following
sample data set?
13 18 16 14 14 12 17 10
Solution:
First, compute the sample mean and the sample standard
deviation. The sample mean is
̅
= 14.25, and the sample standard deviation
is
= 2.6592 to four decimal places. We can use the
Basic Statistics
workbook to compute these values.
Figure 4-1
shows these values when the
data set is entered into the Data 1 column of the workbook.