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Chapter 4: Measures of Position
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The most commonly used measures of position or location are the
z
-score or
the standard score and percentiles. These measures will be discussed in this
chapter along with some special percentiles.
4-2 The
z
-
S
core or Standard Score
Following are a couple of notes when dealing with
-scores.
Notes:
When computing the value of the
-score, the data values can be
either population values or sample values.
Hence one can compute a
z
-score for either population or sample data
values.
The computational formulas for the
-score for when we have sample and
population data are given next.
The computational formula for a
-
score corresponding to a sample value
is given below. In the formula,
̅
represents the sample mean and
represents the sample standard deviation.
The corresponding computational formula for a
-
score corresponding to a
population value
x
is given below. In the formula,
represents the
population mean and
represents the population standard deviation.