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Instructor : Rama Prasada Mohapatra Department of Geography University of Wisconsin-Milwaukee email: [email protected]
University of Wisconsin-Milwaukee
Geography 247
Quantitative Analysis in Geography
Fall 2008
Week 3: Frequency distributions and graphs
University of Wisconsin-Milwaukee
**1. Introduction
- Organizing data
- Histograms, Frequency polygons, and**
Ogives
4. Other types of graphs
Outline
Data
Qualitative/ Categorical
Quantitative/ Numerical
Discrete Continuous
Examples:
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
1. Introduction
Data types
Examples:
Examples:
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
1. Introduction
Measurement scale
Interval Data
Ordinal Data
Nominal Data
Quantitative Data
Qualitative Categories (no Data ordering or ranking)
Ordered Categories (rankings, order, or scaling)
Differences between measurements but no true zero
Ratio Data
Differences between measurements, true zero exists
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
1. Introduction
Need for data organization
- Data (raw) stored in spreadsheets are usually not easy to make inferences
- To draw conclusions the data must be organized in some meaningful way
- The most convenient method of organizing data is to construct a frequency distribution
- The most useful method of presenting data is by constructing charts and graphs
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
1. Introduction
Presenting qualitative data
Categorical Data
Graphing Data
Pie Chart
Bar Chart
Frequency Distribution Table
Tabulating Data
Pareto Diagram
University of Wisconsin-Milwaukee
1. Introduction
Presenting quantitative data
Numerical Data
Stem-and-Leaf Display
Histogram Ogive
Frequency Distributions and Cumulative Distributions
University of Wisconsin-Milwaukee
2. Organizing Data
Frequency distributions
- A frequency distribution is a list or a table consisting of classes and their corresponding frequencies.
- Class is a quantitative or qualitative category in which the raw data is placed
- The frequency of the class is the number of data values contained in a specific class
- It is a way to condenses the raw data into a more useful form for summarization and quick visual interpretation
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
2. Organizing Data
Frequency distributions
- Definition: Frequency distribution
- A frequency distribution is the organization of raw data in table form, using classes and frequencies
- Categorical
- Used for data that can be placed in specific categories (nominal or ordinal level data)
- Grouped
- When the range of the data is large data is grouped into classes that are more than one unit in width
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
2. Organizing Data
Frequency distributions
- Class limits
- Lower class limit
- Upper class limit
- Class boundaries
- Upper class boundaries
- Lower class boundaries
Class limits should have the same decimal place value as the data, but the class boundaries should have one additional place value and end in a 5.
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
2. Organizing Data
Frequency distributions
- Data range
- Highest value – lowest value
- Class width
- Range/ desired number of classes
- Upper/lower class limit – upper/lower class limit of next class
- Upper class boundary – lower class boundary
- Class midpoint
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
2. Organizing Data
Rules for construction of frequency distribution
- There should be between 5-20 classes, no hard-
and-fast rule
- It is preferable but not necessary that the class width be an odd number (only a suggestion)
- Classes must be mutually exclusive
- The classes must be continuous (no gaps)
- The classes must be exhaustive (enough classes)
- The classes must be equal in width
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3. Histograms, Frequency polygons, and Ogives
The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution. Used to visually represent how many values are below certain upper class boundary
Cumulative frequency graphs or ogives
Cumulative frequency is the sum of the frequencies accumulated up to the upper boundary of a class in the distribution. University of Wisconsin-Milwaukee
3. Histograms, Frequency polygons, and Ogives
Graphs of relative frequencies instead of frequencies are used when the proportion of data values that fall into a given class is more important than the actual number of data values that fall into that class.
Relative frequency graphs
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
3. Histograms, Frequency polygons, and Ogives
Converting frequency into proportion
Relative frequency of a class
frequency of a class / total frequency
Sum of relative frequencies will always be 1
Relative frequency
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
3. Histograms, Frequency polygons, and Ogives
Distribution shapes
Single Peak Flat
Unimodal
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
3. Histograms, Frequency polygons, and Ogives
Distribution shapes
J shaped : few data values on left side and increases as one moves to right Reverse J shaped: opposite of the j-shaped distribution
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
3. Histograms, Frequency polygons, and Ogives
Distribution shapes
Positively skewed Negatively skewed Unimodal Unimodal
University of Wisconsin-Milwaukee
3. Histograms, Frequency polygons, and Ogives
Distribution shapes
Bimodal
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3. Other Types of Graphs
Misleading graphs
Scale of the graph
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
3. Other Types of Graphs
Misleading graphs
Two dimensional representation
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
3. Other Types of Graphs
Misleading graphs
Omission of labels or units
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
4. Other Types of Graphs
Several other types of graphs are often used in statistics. We will discuss three other types of graphs as follows:
1. The Pareto chart 2. The Time series graph 3. The Pie graph
Quantitative Analysis in Geography
University of Wisconsin-Milwaukee
4. Other Types of Graphs
A Pareto chart is used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest.
Pareto chart
When the variable displayed on the horizontal axis is qualitative or categorical, a Pareto chart can be used
