Distribution of Quantitative Variables: Learn It 1

  • Describe the graph of a data set using its shape, center, spread, and outliers

Describing Distribution

We can use different graphs, such as dotplots and histograms, to summarize the distribution of a quantitative variable. By displaying the data in such graphs, we can describe features of the distribution of the quantitative variable. The features used to describe the distribution of a quantitative variable are: Shape, center, spread, and presence of outliers. Let’s look at the species and size measurements of [latex]342[/latex] penguins found foraging near Palmer Station, Antarctica.

Black and white penguins in a group walking across sand away from waves of water.
Figure 1. Field data on penguins, like body size and species type, can be graphed and analyzed to explore the shape, center, and spread of distributions.

Shape

To describe the shape of a distribution, imagine sketching the outline of the data to emphasize the general trend. The description of shape includes two parts: the overall pattern and the number of peaks.

overall shape pattern
(left-skewed, symmetric, right-skewed)

Left-skewed: A cluster of data on the right with a tail of data tapering off to the left. A left-skewed distribution has a lot of data at higher variable values with smaller amounts of data at lower variable values.

Symmetric (also called bell-shaped): A cluster of data with a central peak where the left and right sides of the distribution closely mirror each other. If you drew a vertical line down the center of the distribution and folded it in half, the left and right sides would basically match. A bell-shaped distribution has a lot of data in the center, with smaller amounts of data tapering off in each direction.

Right-skewed: A cluster of data on the left with a tail of data tapering off to the right. A right-skewed distribution has a lot of data at lower variable values with smaller amounts of data at higher variable values.

Three clusters of data. On the left side there is an image of left-skewed data, in the center there is a cluster of symmetric data, and on the right side there is right-skewed data.
Figure 2. These three histograms show common distribution shapes—left-skewed, symmetric, and right-skewed—each with different patterns in how the data is spread.

number of peaks
(unimodal, bimodal, multimodal, uniform)

Unimodal: There is one prominent peak.

Bimodal: There are two prominent peaks.

Multimodal: There are three or more prominent peaks.

Uniform: There are no prominent peaks. A rectangular shape, with the same amount of data for each variable value.

Four different graphs showing different peaks. From the top left to right there is unimodal and bimodal peaks shown, and on the bottom left to write shows multimodal and uniform data.
Figure 3. These histograms show four types of distribution shapes based on the number of peaks: unimodal, bimodal, multimodal, and uniform.
Create a histogram for the data set “Penguins – Body Mass” using the Describing and Exploring Quantitative Variables tool.

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