How to Describe Data Patterns in Statistics
Graphic displays are useful for seeing patterns in data. Patterns
in data are commonly described in terms of:
center, spread, shape, and unusual features.
Some common distributions have special descriptive labels, such as
symmetric, bell-shaped, skewed, etc.
Graphically, the center of a distribution is located at the
of the distribution. This is the point in a graphic display where
about half of the observations are on either side. In the chart to the
right, the height of each column indicates the frequency of observations.
Here, the observations are centered over 4.
The spread of a distribution refers to the variability of the
data. If the observations cover a wide
range, the spread is
larger. If the observations are clustered around a single value, the
spread is smaller.
Consider the figures above. In the figure on
the left, data values range from 3 to 7; whereas in the figure on the right,
values range from 1 to 9. The figure on the right is more
variable, so it has the greater spread.
The shape of a distribution is described by the following
- Uniform. When the observations in a set of
data are equally spread across the range of the distribution,
the distribution is called a uniform distribution.
A uniform distribution has no clear peaks.
Here are some examples of distributions and shapes.
Sometimes, statisticians refer to unusual features in a set of data.
The two most common unusual features are gaps and outliers.
- Outliers. Sometimes, distributions are
characterized by extreme values that differ greatly from
the other observations. These extreme values are called
outliers. The second figure below illustrates a distribution
with an outlier. Except for one lonely observation (the outlier
on the extreme right), all of the observations fall between 0 and 4.
As a "rule of thumb", an extreme value is often considered to be an
outlier if it is at least 1.5
interquartile ranges below the first
quartile (Q1), or
at least 1.5 interquartile ranges above the third quartile (Q3).