Let’s Summarize

In "Distributions for Quantitative Data," we focused on describing the distribution of a quantitative variable.

In a graph that summarizes the distribution of a quantitative variable, we can see
- the possible values of the variable.
- the number of individuals with each variable value or interval of values.
To analyze the distribution of a quantitative variable, we described the overall pattern of the data (shape, center, spread), and any deviations from the pattern (outliers).
- We described the shape of a distribution as left-skewed, right-skewed, symmetric with a central peak (bell-shaped), or uniform. Not all distributions have a simple shape that fits into one of these categories.
- The center of a distribution is a typical value that represents the group. We will discuss more precise ways to identify the center of a distribution soon.
- The spread of a distribution is a description of how the data varies. One measurement of spread is the overall range of the data (largest value – smallest value). We also looked at a typical range of values. We will discuss more precise ways to identify a typical range soon.
- Outliers are data points that fall outside the overall pattern of the distribution. We will discuss a more precise way to identify outliers soon.
We used two types of graphs to analyze the distribution of a quantitative variable:
- Dotplots
- Histograms
Following are some observations about dotplots:
- Individual variable values are visible, particularly when the data set is small.
- Descriptions of shape, center, and spread are not affected by how the dotplot is constructed.
- We can accurately calculate the overall range (largest value – smallest value).
Following are some observations about histograms:
- Individual variable values are not visible.
- Grouping individuals into bins of equal-sized intervals is particularly useful when analyzing large data sets.
- We can easily use percentages, also called relative frequencies, to describe the distribution.
- Descriptions of shape, center, and spread are affected by how the bins are defined.
How do we decide when to use a dotplot and when to use a histogram? There are no rules here. Each type of graph can highlight different aspects of the data.

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