Statistics How To

Shapes of Distributions: Definitions, Examples

Descriptive Statistics > Shapes of Distributions

What Defines Shapes of Distributions?

When a data set is graphed, each point is arranged to produce one of dozens of different shapes. The distribution shape can give you a visual which helps to show how the data is spread out, where the mean lies, what the range of the data set it, and many other useful statistics. Shapes of distributions are defined by several different factors:

1. Number of peaks

The peaks are called modes. The mode tells you that the data count is higher in these areas. A unimodal distribution has one mode, a bimodal distribution has two modes and a multimodal distribution has three modes or more.

bimodal distribution

Bimodal distribution. Image credit: Maksim|Wikimedia Commons



This is the same as the mode in descriptive statistics (i.e. the most common number): the peak contains the most common number in the set.

2. Symmetry

A symmetric graph has two sides that are mirror images of each other. The normal distribution is one example of a symmetric graph.

The normal distribution.

The normal distribution.


3. Skewness

Shapes of distributions can differ in skewness; these distributions are not symmetrical. Instead, they have long tails either in the negative direction on the number line (a negative, or left skew) or in the positive direction on the number line (a positive, or right skew). For more on how skewness affects shapes of distributions, see: Skewed Distribution in Statistics.

shapes of distributions

A Left-skewed, negative distribution with a long tail in the negative direction of the number line.



The tails of a distribution (i.e. how thin or fat they are) can also be described by kurtosis, which is measured against the standard normal distribution. A positive value for kurtosis means you have a large peak and little data in the tails. A negative value means you have a flattened peak with lots of data in the tails.

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Shapes of Distributions: Definitions, Examples was last modified: October 12th, 2017 by Stephanie Glen