Assessing Normality
Assessing Normality
The Normal distributions provide good models for
some distributions of real data. Many statistical inference
procedures are based on the assumption that the
population is approximately Normally distributed.
Consequently, we need a strategy for assessing
Normality.
Plot the data.
•Make a dotplot, stemplot, or histogram and see if the
graph is approximately symmetric and bell-shaped.
Check whether the data follow the 68-95-99.7 rule.
•Count how many observations fall within one, two, and
three standard deviations of the mean and check to see if
these percents are close to the 68%, 95%, and 99.7%
targets for a Normal distribution.
Normal Probability Plots:

A normal probability plot is a scatter plot of
the (normal score*, observation) pairs.

Most software packages (including your TI-8X) can construct
Normal probability plots. These plots are constructed by
plotting each observation in a data set against its
corresponding percentile’s z-score.
Interpreting Normal Probability Plots
If the points on a Normal probability plot lie close to a straight
line, the plot indicates that the data are Normal. Systematic deviations
from a straight line (such as curvature in the plot) indicate a nonNormal distribution. Outliers appear as points that are far away
from the overall pattern of the plot.
Normal Probability Plot Example
Ten randomly selected couch potatoes were each asked to list
how many hours of television they watched per week. The
results are:
82
66
90
84
75
88
80
94
110
91
Use your graphing calculator to verify normality:
1. Enter the data into a list
2. Open the Stat Plot menu, turn a plot on, and select the last option
under Type.
3. Hit Zoom 9
(Minitab obtained the normal probability plot on the following slide.)
5
Normal Probability Plot Example
6
Notice that the points all fall nearly on a line so it is
reasonable to assume that the population of hours of
TV watched by couch potatoes is normally distributed.
EXAMPLE
A sample of times of 15 telephone solicitation calls (in
seconds) was obtained and is given below.
5
10
7
12
35
65
145
14
3
220
11
6
85
6
16
Construct your own plot to verify
normality.
Normal Probability Plot Example
Clearly the points do not fall
on a line. Specifically the
pattern has a distinct nonlinear
(perhaps logarithmic)
appearance. It is NOT
reasonable to assume that the
population of telephone
solicitation calls is normally
distributed.
One would most assuredly
say that the distribution of
lengths of calls is not
normal.
8