Organizing Data

Topic 2: Organizing and Displaying Data

Overview

  • Frequency Distributions

    • Ungrouped

    • Grouped (Class intervals)

  • Graphs

    • Frequency Histograms

    • Frequency Polygons

    • Bar Graphs

  • Excel Exercise to create a histogram (Horvath p. 53-70)

Organizing and Displaying Data

  • Purpose: To simplify and make sense of large data sets

  • Method:

    • Frequency Distribution: Lists all possible data values and the frequency of their occurrence

    • Organizes and describes data in table form and used to construct frequency histograms (graphs)

    • Reveals patterns in scores/observations

Types of Frequency Distributions

a) Ungrouped

  • Description:

    • Frequency of all possible data values/items in a dataset.

    • Can be nominal/ordinal categories or quantitative with a small number of values.

  • Examples:

    • Categorical: Blood type, Majors, Teams.

    • Quantitative: Number of kids in a household, number of places lived in.

b) Grouped (Class Intervals)

  • Description:

    • Used when there are too many possible data values

    • Data is organized into groups called class intervals, each covering a range of data.

Examples of Ungrouped and Grouped Frequency Distributions

Ungrouped examples:

  • Categorical: Blood type, Majors, Teams

  • Quantitative: Household members, places lived

Grouped examples:

  • Continuous values: Annual salary, reaction times, weight, commuting time

  • Can be discrete

Frequency Distribution Example: Ungrouped

  • Chin-up scores:

    • Scores: 7, 15, 14, 9, 8, 13, 12, 15, 8, 12, 9, 9, 10, 13, 11, 10, 12

    • Frequency and tally marks:

      • 15: II (2)

      • 14: I (1)

      • 13: II (2)

      • 12: III (3)

      • 11: I (1)

      • 10: II (2)

      • 9: III (3)

      • 8: II (2)

      • 7: I (1)

Steps in Constructing a Frequency Distribution

  1. Count the Number of Scores: N = 50.

  2. Identify Highest and Lowest Score:

    • Use Excel to identify MAX and MIN or sort dataset.

    • Example: MAX = 368, MIN = 252; Range = 116.

  3. Identify Smallest Unit of Measurement: The smallest unit of measurement used is 1.

  4. Decide on the Number of Class Intervals:

    • Estimate number of bins; can adjust as necessary.

    • N = 50 suggests interval of 7.

  5. Decide on Score Range for Each Class Interval:

    • Use formula for class interval (i).

    • Example: i = (Highest - Lowest) / (number of categories).

  6. Round to Make Range Appealing:

    • Choose 'pretty' numbers for class intervals.

  7. List Class Intervals in Order:

    • Ensure intervals are consistent, non-overlapping, and cover all data.

Ungrouped Distributions

Use UNGROUPED:

  • When data consists of items rather than numbers (nominal or ordinal values)

  • When there are fewer than 15 possible discrete scores.

Grouped Distributions

Use GROUPED:

  • For continuous data values or too many possible values (e.g., age, salary).

  • Estimated starting number of bins should be adjusted based on analysis needs.

Example Exercise

  • Construct frequency distribution for: RTs for participants: .31, .27, .28, .29, .30, .25, .26, .27, .31, .34, .27, .28, .28, .29, .32.

Histogram and Graphs

  • Definition: Pictorial representation of frequency distribution data.

  • Types of Graphs:

    1. Bar Graphs for Grouped Data

    2. Histograms for Ungrouped Data

Bar Graphs

  • Represents frequencies or group statistics

  • x-axis shows groups; order does not matter (nominal) and bars are separated by spaces

Histogram

  • Vertical bars depict frequencies of interval/ratio variables

  • No spacing between bars; used for grouped data

Excel Exercises

  1. Enter data in Excel.

  2. Use Data Analysis tool to create histograms.

  3. Format histogram by adding titles and adjusting charts for clarity.