Essential Statistics

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154 Chapter 4: Measures of Position
Observe that the distance between the mean of 99.3333 and the value of 90
is 1.42 = 1.42 6.5955  9.3656. Thus, if we subtract the value of 9.3656
from the mean of 99.3333, we will get 99.3333 – 9.3656 = 89.9677  90, the
data value. This shows that the value of 90 is approximately 1.42 standard
deviations below the mean value of 99.3333.
That is, a negative z-score for a data value gives us an idea of how far the
value is below the mean, and so it gives us an idea of the position of the data
value relative to the mean.
From both examples, one can infer that a z-score tells how many
standard deviations above or below the mean the value will be
located and so it gives us an idea of the position of the data value
relative to the mean.
Section Review
4-3 Percentiles
In this section we will discuss percentiles, the very important measure of
position . You probably may recall from high school that your ACT or SAT
scores were given in terms of percentiles. Here we will study how
percentiles are computed and why we use a percentile as a measure of
position.
First we will define what we mean by percentiles.
Definition: Percentiles
Percentiles are numerical values that divide an ordered data set into 100
groups of values with at most 1% of the data values in each group.