Ef 507 quantitative methods for economics and finance

• EF 507

• QUANTITATIVE METHODS FOR ECONOMICS AND FINANCE

• FALL 2008

• Chapter 2

• Describing Data: Graphical

Chapter Goals

• After completing this chapter, you should be able to:

• Identify types of data and levels of measurement

• Create and interpret graphs to describe categorical variables:

• bar chart, pie chart

• Create a line chart to describe time-series data

• Create and interpret graphs to describe numerical variables:

• Histogram
• Construct and interpret graphs to describe relationships between variables

• Describe appropriate and inappropriate ways to display data graphically

Types of Data

Measurement Levels

Graphical Presentation of Data

• Data in raw form are usually not easy to use for decision making

• Some type of organization is needed

• Table
• Graph

• The type of graph to use depends on the variable being summarized

Graphical Presentation of Data

• Techniques reviewed in this chapter:

Tables and Graphs for Categorical Variables

The Frequency Distribution Table

Bar and Pie Charts

• Bar charts and Pie charts are often used for qualitative (category) data

• Height of bar or size of pie slice shows the frequency or percentage for each category

Bar Chart Example

Pie Chart Example

Pareto Diagram

• Used to portray categorical data

• A bar chart, where categories are shown in descending order of frequency

• A cumulative polygon is often shown in the same graph

• Used to separate the “vital few” from the “trivial many”

Pareto Diagram Example

• Example: 400 defective items are examined

• for cause of defect:

Pareto Diagram Example

• Step 1: Sort by defect cause, in descending order

• Step 2: Determine % in each category

Pareto Diagram Example

Graphs for Time-Series Data

• A line chart (time-series plot) is used to show the values of a variable over time

• Time is measured on the horizontal axis

• The variable of interest is measured on the vertical axis

Line Chart Example

Graphs to Describe Numerical Variables

Histogram

• A graph of the data in a frequency distribution is called a histogram

• The interval endpoints are shown on the horizontal axis

• the vertical axis is either frequency, relative frequency, or percentage

• Bars of the appropriate heights are used to represent the number of observations within each class

Histogram Example

Histograms in Excel

• Select

• Tools/Data Analysis

Choose Histogram

• Choose Histogram

Questions for Grouping Data into Intervals

• 1. How wide should each interval be? (How many classes should be used?)

• 2. How should the endpoints of the intervals be determined?

• Often answered by trial and error, subject to user judgment
• The goal is to create a distribution that is neither too "jagged" nor too "blocky”
• Goal is to appropriately show the pattern of variation in the data

How Many Class Intervals?

• Many (Narrow class intervals)

• may yield a very jagged distribution with gaps from empty classes
• Can give a poor indication of how frequency varies across classes

• Few (Wide class intervals)

• may compress variation too much and yield a blocky distribution
• can obscure important patterns of variation.

Distribution Shape

• The shape of the distribution is said to be symmetric if the observations are balanced, or evenly distributed, about the center.

Distribution Shape

• The shape of the distribution is said to be skewed if the observations are not symmetrically distributed around the center.

Relationships Between Variables

• Graphs illustrated so far have involved only a single variable

• When two variables exist other techniques are used:

Scatter Diagrams are used for paired observations taken from two numerical variables

• Scatter Diagrams are used for paired observations taken from two numerical variables

• The Scatter Diagram:

• one variable is measured on the vertical axis and the other variable is measured on the horizontal axis

Scatter Diagram Example

Scatter Diagrams in Excel

• Select the chart wizard

Graphing Multivariate Categorical Data

• Side by side bar charts

Side-by-Side Chart Example

• Sales by quarter for three sales territories:

Data Presentation Errors

• Goals for effective data presentation:

• Present data to display essential information

• Communicate complex ideas clearly and accurately

• Avoid distortion that might convey the wrong message

Data Presentation Errors

• Unequal histogram interval widths

• Compressing or distorting the vertical axis

• Providing no zero point on the vertical axis

• Failing to provide a relative basis in comparing data between groups

Chapter Summary

• Reviewed types of data and measurement levels

• Data in raw form are usually not easy to use for decision making -- Some type of organization is needed:

•  Table  Graph

• Techniques reviewed in this chapter:

• Frequency distribution
• Bar chart
• Pie chart
• Pareto diagram

Which of the following variables is an example of a categorical variable?

• Which of the following variables is an example of a categorical variable?

• A. The amount of money you spend on eating out each month.

• B. The time it takes you to write a test.

• C. The geographic region of the country in which you live.

• D. The weight of a cereal box.

The data in the time series plot below represents monthly sales for two years of beanbag animals at a local retail store (Month 1 represents January and Month 12 represents December). Do you see any obvious patterns in the data? Explain.

• The data in the time series plot below represents monthly sales for two years of beanbag animals at a local retail store (Month 1 represents January and Month 12 represents December). Do you see any obvious patterns in the data? Explain.

• This is a representation of seasonal data. There seems to be a small increase in months 3, 4, and 5 and a large increase at the end of the year. The sales of this item seem to peak in December and have a significant drop off in January.

At a large company, the majority of the employees earn from $20,000 to $30,000 per year. Middle management employees earn between $30,000 and $50,000 per year while top management earn between $50,000 and $100,000 per year. A histogram of all salaries would have which of the following shapes?

• At a large company, the majority of the employees earn from $20,000 to $30,000 per year. Middle management employees earn between $30,000 and $50,000 per year while top management earn between $50,000 and $100,000 per year. A histogram of all salaries would have which of the following shapes?

• a. Symmetrical

• b. Uniform

• c. Skewed to right

• d. Skewed to left