
A Standard Normal Distribution
With Nine Specific Intervals

 There exists a normal distribution with a mean
of 0 and a standard deviation of 1. It is called the standard normal distribution.


 When the center interval is within a quarter of a standard
deviation of the mean, and each of the other intervals are a half standard deviation wide (exclusive of
the tails), the distribution has been marked in stanines  the standard nine intervals.
It is often used to:  compare two or more distributions of data, particularly test scores.
 estimate or to compute probabilities of events involving normal distributions,
 facilitate using words rather than numbers in presenting statistical data.
 [Click on graphic to go to a printable copy.]

 The standard normal distribution and scale may be thought of
as a tool to scale up or down another normal distribution.

 The standard normal distribution is a tool to
translate a normal distribution into numbers which may be used to learn more information about the set of
data than was originally known.

 The stanine interevals are a tool to put descriptive words in
place of numbers and also to create enough intervals so that conversation about and comparison of two
or more sets of scores is meaningful.

 It is still a standard normal distribution, so the
same notations and variables hold: a standard normal scores (z),
the normal distribution mean (either
or µ), the normal distribution standard deviation, (either s or
), and the normal distribution scores (x), are used and
 and
.

 The difference is now words and less accuracy are used. For example:

 "Terry tested considerably above average."

 That means his/her score was in the 7th stanine.
