Organizing and Displaying Data

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)

Frequency Distribution

• Definition: A frequency distribution lists all possible data values or types and the frequency of occurrence of each.
• Purpose: Organize and describe data in table form.
• Can be used to construct a frequency histogram to visualize data patterns.

Types of Frequency Distributions

A) Ungrouped Distribution

• Characteristics:

  • Lists frequency of all possible data values in the dataset.
  • Can be qualitative (nominal/ordinal) or quantitative (small sets of values).

• Examples:

  • Categorical: Blood Types, Majors, Teams
  • Quantitative: Number of kids in a household, Towns lived in.

B) Grouped Distribution (Class Intervals)

• When to Use:

  • When the dataset contains too many possible values to list individually.
  • Data is ranged across intervals for organization.

• Examples:

  • Annual salary, Reaction times, Weight, Commuting time.
  • Can include continuous values or discrete (e.g., age).

Creating Ungrouped Frequency Distribution

• Example Data: Chin-up scores: 7, 15, 14, 9, 8, 13, 12, 15, 8, 12, 9, 9, 10, 13, 11, 10, 12




• Frequency Table:
  

  Score (X)	Tally	Frequency
  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

Cumulative Frequency Distribution Example

Grouped Frequency Distribution

• Steps to Construct:

1. Count the Scores: Total N = 17.
2. Identify Highest and Lowest Scores: (MAX = 15, MIN = 7) gives a range = 8.
3. Identify Smallest Unit of Measurement: Smallest = 1.
4. Decide Number of Class Intervals (e.g., 5).
5. Determine Class Interval Width ($i$): Use formula for width, e.g., $i = \frac{MAX - MIN}{n}$.
6. Rounding/Adjusting Width (to make a prettier class interval).
7. List Out Class Intervals: e.g., 6-7, 8-9, 10-11…

Types of Distributions

Ungrouped Distributions

• Used for nominal/ordinal values or when items are few (< 15).

Grouped Distributions

• Used for continuous values (e.g., weight, height) or when there are too many values.
• Class intervals are calculated to effectively group data.

Graphs and Histograms

Bar Graphs

• Used for grouped data.
• Categories on the x-axis with spaces in between bars.

Histograms

• Used for ungrouped data.
• No spaces between bars, showing frequencies of interval/ratio data.

Excel Exercise for Creating Histograms

1. Enter data in Excel.
2. Select Tools/Data Analysis.
3. Choose Histogram from Analysis Tools.
4. Input data and class intervals.
5. Format the histogram to add title and labels, ensuring bars meet proper spacing for interval/ratio data.