STAT200 Lecture 2 Notes

STAT200 LECTURE 2 Notes

Tabular and Graphical Displays: Categorical One-Variable Case

  • Prof. Angela Mak
Introduction to Descriptive Statistics

  • Descriptive statistics summarize data to make it easy to understand. Common measures include:

    • Mean
    • Variance

  • Data visualization methods include:

    • Tabular Displays
    • Graphical Displays
Types of Categorization for Data

  1. Tabular Displays

    • Frequency Distribution
    • Relative Frequency Distribution
    • Percent Frequency Distribution
    • Crosstabulation

  2. Graphical Displays

    • Bar Chart
    • Pie Chart
    • Side-by-Side Bar Chart
    • Stacked Bar Chart
Focus on Categorical Data

  • We will begin with the one-variable case and discuss appropriate displays:

    • Tabular Displays:

    • Frequency Distribution

    • Relative Frequency Distribution

    • Percent Frequency Distribution

    • Graphical Displays:

    • Bar Chart

    • Pie Chart

Frequency Distribution
  • Definition: A frequency distribution is a tabular summary showing the number (frequency) of observations in each of several non-overlapping categories or classes.
RatingFrequency
Poor2
Below Average3
Average5
Above Average9
Excellent1
Total20
Relative Frequency and Percent Frequency Distributions

  • Relative Frequency: The fraction or proportion of the total number of observations that belong to a specific class.

  • Percent Frequency: The relative frequency multiplied by 100, expressed in percentage.

RatingRelative FrequencyPercent Frequency
Poor0.1010%
Below Average0.1515%
Average0.2525%
Above Average0.4545%
Excellent0.055%
Total1.00100%
Bar Chart
  • Definition: A bar chart is a graphical display used to depict qualitative data.
  • The vertical axis can represent frequency, relative frequency, or percent frequency.
  • Bars are separated to emphasize the individuality of each category.
Pie Chart
  • Definition: A pie chart is often used to present relative frequency and percent frequency distributions.
  • A circle represents 360 degrees; for example, a class with a relative frequency of 0.25 corresponds to:
    0.25×360=90 degrees0.25 \times 360 = 90 \text{ degrees} of the circle.
Creating Pivot Tables and Charts for Categorical Data
  • Steps to Create Pivot Table and Charts:
    1. Click on a cell containing data.
    2. Insert ➔ Pivot Table.
    3. Under the Pivot Chart Fields List:
    • Drag information to Rows and Values (default shows counts).
    1. To create relative and percent frequency, drag the information again and adjust value field settings to display as "% of grand total".
    2. Optionally adjust number format.
    3. Duplicate the Pivot Table to another sheet, remove unwanted elements, then create the Pivot Chart for visualization.