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Understanding Ungrouped and Grouped Frequency Distributions in Data Analysis

This guide provides comprehensive instructions on creating ungrouped and grouped frequency distributions using interval/ratio level data. It outlines the steps for listing all possible values, counting frequencies, and calculating cumulative and percentage frequencies. The guide emphasizes the importance of using APA format for titles and explains the difference between histograms and frequency polygons. Additional techniques like stem-and-leaf plots and cumulative frequency distributions are also covered. Essential for anyone looking to analyze and visualize data effectively.

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Understanding Ungrouped and Grouped Frequency Distributions in Data Analysis

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  1. Tables and Graphs Part II February 2, 2005

  2. What you can do with Interval/Ratio level data… • Ungrouped ‘ratio’ data

  3. Option #1: Ungrouped Frequency Distribution • A table that displays all the possible values for this variable along with the frequency of occurrence for each value. • List all values between the minimum and maximum scores in column 1 • Count the number of subjects who obtained each value and place the frequency in column 2. • Columns 3, 4, etc. may include %, cumulative %, cumulative frequency, etc.

  4. Step #3 Compute the % frequency for each value (determines the Mode) How to create an Ungrouped Frequency Distribution Step #4 Compute the cumulative frequency Step #1 List all values between the minimum and maximum scores in column 1. Do not skip any! Step #5 Compute the cumulative percent (determines the Median) Step #2 Count the number of subjects who obtained each value and place the frequency in column 2. Step #6 Create a title for the table… be sure to use APA format.

  5. Histogram vs. Frequency Polygon

  6. Grouped Frequency Distribution • A table that displays the frequency of occurrence in “intervals” • The number of intervals should be <15 • Logic and convention play the most important roles when determining the number of intervals

  7. Steps for creating a Grouped Frequency Distribution • Determine range (Range = High Score - Low Score) • Determine interval width • Width=Range/15 • Round the width up or down to a reasonable/logical number • Determine the lowest interval, create mutually exclusive and exhaustive categories • Count the number of scores (f) that fall in each interval • Use the same procedures the were used for creating an ungrouped table

  8. Step #3 Determine the lowest interval, create mutually exclusive and exhaustive categories Grouped frequency distribution for the Honolulu Heart Study Data Range=91-47=44 Step #4 Count the number of scores (f) that fall in each interval Width = 44/15 = 2.9333 Round to 3 Step #1 Determine range (Range = High Score - Low Score) Step #5 Decide if this interval width is the best way to display your data. Modify the table accordingly Choices for lowest interval: 47-49 46-48 45-47 Step #2 Determine interval width Width=Range/15 Round the width up or down

  9. Histograms & Frequency Polygons for Grouped Data

  10. Histograms & Frequency Polygons for Grouped Data

  11. 3D Histograms & Frequency Polygons for Grouped Data

  12. 3D Histograms & Frequency Polygons for Grouped Data

  13. The Stem-and-Leaf Plot • Each number in the data set is broken into two pieces called a stem and a leaf. • Stem • The first part of the number • Consists of the beginning digit(s) • Leaf • The last part of the number • Consists of the final digit(s) Example: 213 (stem=2, leaf=13) or (stem=21, leaf=3)

  14. Matching variables to graphs that represent the raw data values

  15. Cumulative Frequency Distribution (also called an Ogive curve)

  16. For Friday… • Practice • Practice • Practice

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