Please read this and give reflection on thoughts: One problem with means and sta

Please read this and give reflection on thoughts:
One problem with means and standard deviations is that they do not convey enough
information for us to make meaningful assessments or accurate interpretations of
Data.
Other metrics are designed for more exact interpretations. The Z score trans-
forms data into standardized units that are easier to interpret. A Z score is the differ-
ence between a score and the mean, divided by the standard deviation:
Z 5 Xi 2 X
S
In other words, a Z score is the deviation of a score Xi from the mean in standard
deviation units. If a score is equal to the mean, then its Z score is 0. For example,
suppose the score and the mean are both 6, then 6 2 6 5 0. Zero divided by any-
thing is still 0. If the score is greater than the mean, then the Z score is positive; if
the score is less than the mean, then the Z score is negative.
Let’s try an example. Suppose that Xi 5 6, the mean X 5 3, and the standard
deviation S 5 3. Plugging these values into the formula, we get
Z 5 6 2 3
3 5 3
3 5 1
Let’s try another example. Suppose Xi 5 4, X 5 5.75, and S 5 2.11. What is
the Z score? It is 2.83:
Z 5 4 2 5.75
2.11 5 21.74
2.11 5 2.83
Terms and Symbols Used to Describe Populations and Samples
Population Sample
Definition All elements with
the same definition
A subset of the population,
usually drawn to represent
it in an unbiased fashion
Descriiptive characteristics Parameters Statistics
Symbols used to describe Greek Roman
Symbol for mean m X
Symbol for standard deviation s S
2.3 PSYCHOLOGICAL TESTING IN EVERYDAY LIFE
Z 5 Xi 2 X
S
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CHAPTER 2 ● Norms and Basic Statistics for Testing 41
This means that the score we observed (4) is .83 standard deviation below the av-
erage score, or that the score is below the mean but its difference from the mean is
slightly less than the average deviation.