4.2 Presenting Quantitative Data Graphically

4.2 Presenting Quantitative Data Graphically

Learning Objectives

  • Upon completion of this section, students should be able to:

    • Create and interpret Histograms.

    • Create and interpret frequency polygons.

    • Create and interpret basic stem and leaf displays.

    • Identify common graphical mistakes with the graphical representation of quantitative data.

Overview of Quantitative Data

  • Definition: Quantitative data (or numerical data) refers to data that can be expressed as a quantity or a measurement.

  • Examples of Quantitative Data:

    • Height

    • Weight

    • Response time

    • Subjective rating of pain

    • Temperature

    • Exam scores

  • Distinction: Quantitative data differs from categorical (qualitative) data, which includes variables such as favorite color, religion, city of birth, and favorite sport, where no ordering or measurement is involved.

Creating Frequency Tables

  • Concept: Just as with categorical data, we can create frequency tables for quantitative data.

  • Example 1: A teacher notes scores from a 20-point quiz for 30 students:

    • Scores:

    • 19, 20, 18, 18, 17, 18, 19, 17, 20, 18, 20, 16, 20, 15, 17, 12, 18, 19, 18, 19, 17, 20, 18, 16, 15, 18, 20, 5, 0, 0

    • Frequency Table Construction:

    • The score represents the categories for the bars in the graph.

    • Count how many of each score occurs and record these in the frequency column.

Graphing with Bar Charts

  • A standard bar chart can be created based on the frequency table derived from the quiz scores.

  • Issue with Bar Graphs: A bar chart may not be appropriate for displaying quantitative data as it may obscure meaningful differences between scores due to unequal intervals.

  • Improvement: Use a histogram instead, where the horizontal axis functions as a number line, thus preserving gaps between score categories.

Explanation of Histograms

  • Definition: A histogram is similar to a bar graph, but it represents class intervals or ranges of numeric values squared for the data observations.

  • Construction Guidelines:

    • Each interval is equal in width.

    • Aim for between 5 and 20 class intervals depending on the volume of data.

    • Data values fit into a specific class without overlap.

  • **Example of Histogram Representation:

    • The first bar on a histogram represents values between the lower limit (0) and the upper limit (1), indicating frequency for that range.

  • Key Characteristics: When constructing histograms, it is crucial to define lower and upper class limits, ensuring clarity and avoiding gaps when needed.