This module examines a batch of numbers (i.e., the data) to determine if they are normally distributed. The techniques are graphical and informal.

The normal distribution is the most used distribution in statistics. The principal reasons are:

- Normality arises naturally in many physical, biological, and social measurements.
- Normality is important in statistical inference.

The *q ^{th}* sample quantile is a value along the
measurement scale with a proportion

The normal quantile plot implemented in `JavaStat`
incorporates the features of a box and whisker plot. Specifically,
options are available for showing the quartiles and the outlier
cutoffs.

Consider the following data which was generated randomly from a
normal distribution (see the `Normal Distribution` module)
with a mean of 10 and a standard deviation of 2:

12.61, 13.07, 7.36, 8.26, 10.98, 8.43, 11.53, 10.10, 8.89, 8.66, 12.08, 11.26, 11.41, 9.78, 7.23, 13.81, 10.62, 10.49, 8.81, 10.58, 10.60, 10.93, 12.20, 8.28, 6.97, 8.12, 9.06, 10.49, 3.84, 12.05This list of numbers does not give us much insight into the underlying normal probability law that generated the data. However, a graphical view of the data, as seen below in the

The `Normal Plot` can be enhanced by items in the
`Options` menu. Select `Robust Fit` from the
`Options` menu to fit a line to the data. If the data is
normally distributed it should fall along this line. It appears that
the data is normally distributed except possibly the value in the
lower left corner.

Quantile lines can be superimposed on the plot by selecting
`Quantiles lines` from the `Options` menu. If an
outlier is present, red outlier lines are drawn. Since no red lines
are visible, the value in the lower left corner is not an outlier.

Example #1 examines the distribution of student distances from Oxford to determine if the distribution is normally distributed using a histogram and normal quantile plot. Various normalizing transformations are explored.

Exercise #1 examines the distribution of FFD from the Aircraft dataset to determine if the distribution is normally distributed using a histogram and normal quantile plot. Various normalizing transformations are explored.