Chapter 2: Summarizing Data in Tables and Graphs

2.1 Organizing Qualitative Data

Qualitative data, also known as categorical data, must be organized to be useful for analysis. This section covers methods for organizing such data using tables and graphical displays.

2.1.1 Organize Qualitative Data in Tables

• Frequency Distribution: A table that lists each category of data and the number of occurrences for each category.

• Relative Frequency: The proportion (or percent) of observations within a category, calculated as:

• Relative Frequency Distribution: A table listing each category with its relative frequency.

• Example: A physical therapist records the body part requiring rehabilitation for 30 patients and organizes the data into a frequency and relative frequency table.

2.1.2 Construct Bar Graphs

• Bar Graph: Categories are labeled on one axis, and frequencies or relative frequencies on the other. Each category is represented by a rectangle of equal width; the height shows the frequency or relative frequency.

• Pareto Chart: A bar graph with bars ordered from highest to lowest frequency or relative frequency.

• Side-by-Side Bar Graphs: Used to compare two data sets, typically using relative frequencies for fair comparison.

• Horizontal Bar Graphs: Useful when category names are lengthy.

• Example: Comparing educational attainment in 1990 and 2017 using side-by-side bar graphs.

2.1.3 Construct Pie Charts

• Pie Chart: A circle divided into sectors, each representing a category. The area of each sector is proportional to the category's frequency.

• Example: Educational attainment data for U.S. residents aged 25+ in 2017 is displayed as a pie chart.

2.2 Organizing Quantitative Data: The Popular Displays

Quantitative data can be discrete or continuous. The method of organization depends on the type and range of data values.

2.2.1 Organize Discrete Data in Tables

• Discrete Data: Data with countable values (e.g., number of customers in a time interval).

• Frequency and Relative Frequency Distributions: Tables summarizing how often each value occurs.

2.2.2 Construct Histograms of Discrete Data

• Histogram: Rectangles represent classes of data. The height shows frequency or relative frequency, and rectangles touch each other to indicate continuity.

2.2.3 Organize Continuous Data in Tables

• Classes: Intervals into which data are grouped for large or continuous data sets.

• Class Limits: Lower class limit is the smallest value in a class; upper class limit is the largest.

• Class Width: The difference between consecutive lower class limits.

• Guidelines: Choose a convenient lower class limit and a class width that results in 5–20 classes. The choice is somewhat subjective and should best summarize the data.

2.2.4 Construct Histograms of Continuous Data

• Histogram for Continuous Data: Similar to discrete, but classes are intervals. The width of each rectangle equals the class width.

• Example: Parking fine data grouped into classes of width 25 and displayed as a histogram.

2.2.5 Draw Dot Plots

• Dot Plot: Each observation is plotted as a dot above its value on a number line. Multiple dots stack vertically for repeated values.

• Example: Number of arrivals at a restaurant plotted as a dot plot.

2.2.6 Identify the Shape of a Distribution

• Uniform Distribution: Frequencies are evenly spread across values.

• Bell-Shaped Distribution: Highest frequency in the middle, tapering off symmetrically.

• Skewed Right: Right tail is longer; most data are on the left.

• Skewed Left: Left tail is longer; most data are on the right.

• Example: Analyzing the shape of a histogram for parking fines.

2.2.7 Draw Time Series Graphs

• Time Series Data: Values measured at different points in time.

• Time-Series Plot: Time is on the horizontal axis, variable values on the vertical axis, with points connected by line segments.

• Example: Plotting the Partisan Conflict Index over time.

2.3 Graphical Misrepresentations of Data

Graphs can be misleading or deceptive if not constructed properly. This section discusses common pitfalls and best practices.

2.3.1 Describe What Can Make a Graph Misleading or Deceptive

• Misleading Graph: Unintentionally creates an incorrect impression.

• Deceptive Graph: Purposely creates an incorrect impression.

• Common Issues:

  • Improper scale (e.g., inconsistent increments, non-zero baseline)

  • Distorted axes or origins

  • Clutter or unnecessary design elements

  • Three-dimensional effects that obscure data

• Guidelines for Good Graphics:

  • Clearly title and label axes, including units and data sources

  • Avoid distortion and minimize white space

  • Indicate truncated scales clearly

  • Avoid clutter and unnecessary backgrounds

  • Use consistent design throughout the graphic

  • Do not use relative graphs without data or scales

• Example: A bar graph starting at 30,000 instead of 0 exaggerates changes in poverty rates.