1. Frequency Distributions and Graphs
Chapter 2 Review
Frequency Distributions and Graphs

2. Organizing Data
In order to describe situations, draw conclusions, or make inferences, data must be organized in a meaningful way
Done through the use of frequency distributions and statistical charts and graphs
Frequency Distribution: organization of raw data in table form, using classes and frequencies

3. Frequency Distribution Types
Categorical Frequency Distribution
Used when the data can be placed in specific categories, such as nominal- or ordinal-level data

4. Frequency Distributions cont.
Grouped Frequency Distributions
Data is grouped into classes that are more than one-unit in width
Used when the range of data values is large

5. Other Distribution Types
Open-Ended distribution
Frequency distribution with an open-ended class
Cumulative distribution
Distribution that shows the number of data values less than or equal to a specific value
Ungrouped Frequency distribution
Used then the range of data is small and single data values are used for each class

6. Properties of Freq. Distribution
Should be between 5 and 20 classes
Class width is preferably an odd number
Classes are mutually exclusive (non-overlapping)
Classes are continuous (no gaps)
Classes are exhaustive (contains all of the raw data)
Classes are equal in width (except open-ended distribution)

7. Constructing a Frequency Distribution
Determine the classes
Find the highest and lowest values
Find the range
Select the number of classes desired
Find the class width (divide range by # of classes desired)
Select a starting point
Find the upper class limits
Find the boundaries
Tally the data
Find the numerical frequencies and the cumulative frequencies

8. Graphs and Charts
Data must be presented in graphical form after it is organized
3 most commonly used graphs are:
Histogram: displays data by using contiguous vertical bars to represent the frequencies of the classes
Frequency Polygon: displays the data by using lines that connect point plotted for the frequency of the midpoints of the classes
Ogive: line graph that represents the cumulative frequencies for the classes

9. Examples

10. Other Types of Graphs
Bar Graphs: represent the data by using vertical or horizontal bars whose heights or lengths represent frequencies of the data

11. Other Types of Graphs cont.
Pareto charts: used to represent a frequency distribution where the bars of the chart are ordered from highest to lowest

12. Other Types of Graphs cont.
Pie graph: circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution

13. Other Types of Graphs cont.
Time-series graph: represents data that occur over a specific period of time
Stem and Leaf plot: data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes

14. Key Words Raw data: data in original form
Class: category that qualitative or quantitative data that raw data is placed into
Lower Class limit: smallest data value that can be included in a class
Upper class limit: largest data value included in a class
Class boundaries: separate the classes so there are no gaps in the frequency distribution

15. Key Words cont.
Class width: difference between the upper and lower class boundaries for each class
Class midpoint: obtained by adding the upper and lower class boundaries and dividing by 2
Outliers: extremely large or small data values compared to the other data values