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
- 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.