Wiki Page, Math 13 - Perez Sandbox : Module 4 - Wrap Up "Distributions for Quantitative Data"

Wiki Page
2026-01-17T21:15:50-08:00

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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