2.4. Distribution Maps

Learning Outcome

Students will be able to identify common distribution models and discern what types of data fit certain models.

Sample Tasks

• Student will be able to create distribution maps of quantitative variables

  • Biological data that fit the normal distribution such as blood pressure, height, and weight

  • Data that does not fit the normal distribution such binomial or Bernoulli distributions

  • Students analyze wait times and build an appropriate distribution map based on their observations.

  • Student will investigate heat maps and choose to highlight different variables.

• Voting patterns:

  • Student will find a large data set of voting information for a certain state or county.

  • Students create maps to display the voting information.

  • Students make a hypothesis about voting patterns in a certain geographic area.

  • Student will analyze the different areas and a manipulate the fineness of measurement to highlight various areas.

  • Based on the observations, the students will verify the hypothesis.

  • Students will describe a future data set that would allow them to confirm their hypothesis.

• Plotting a data set with large variation for a market study

  • Find a data set of ages for customers that visit McDonalds for breakfast

  • Plot the entire data set using an appropriate chart

  • Look for a pattern (we hope that it does not exist)

  • Generate a hypothesis that could pertain to breakfast promotion

  • Break the data into subsets

    • Age range

    • Time of morning

    • Day of the week

  • Replot using the subsets

  • Look for a pattern to verify your hypothesis

  • Summarize the process

  • Present as a marketing pitch

[OhioDoHEducation21]

Our first readings, from Computational and Inferential Thinking [ADW21], are repeated from Section 2.2 and remind us how to plot distributions in 1 variable.

• 7.1. Visualizing Categorical Distributions

• 7.2. Visualizing Numerical Distributions

Our second readings, from Learning Data Science [LGN23], are also repeated from Section 2.2. These remind us how to plot distributions in 1 and 2 variables.

• 10.2. What to Look For in a Distribution

• 10.3. What to Look For in a Relationship

Reading Questions

• What does it mean for a distribution to skew right?

• What does it meant for a distribution to have a long tail?

Our third reading, also from Learning Data Science [LGN23], discusses distributions on geographic maps.

• 11.4.4. Geographic Data

When studying a distribution, one question to ask is how well it fits the distribution of a known statistical model, such as a normal distribution. We will study such statistical models in Section 3.1.

Further Resources

• From the Python Data Science Handbook [Van16]

  • 4. Visualization with Matplotlib

    • Density and Contour Plots

    • Histograms, Binnings, and Density

    • Geographic Data with Basemap

Further Resources

See Section 2.1 for information on plotting with Matplotlib and Seaborn.