<h3 collapsed="false" seolevelmigrated="true">Lecture Overview</h3><ul><li><p><strong>Instructor:</strong> Samuel Wylde</p></li><li><p><strong>Course:</strong> Econ 270: Statistics for Economics</p></li><li><p><strong>Institution:</strong> University of Illinois Chicago (UIC)</p></li><li><p><strong>Term:</strong> Fall 2024</p></li></ul><div data-type="horizontalRule"><hr></div><h3 collapsed="false" seolevelmigrated="true">iClicker Test</h3><ul><li><p><strong>Participation Link:</strong> <a target="_blank" rel="noopener noreferrer nofollow" class="link" href="https://join.iclicker.com/ZMFC" download="true">Join iClicker</a></p></li><li><p><strong>Example Question:</strong> License plate numbers are an example of:</p><ul><li><p>a) Categorical, ordinal variable</p></li><li><p>b) Categorical, nominal variable</p></li><li><p>c) Categorical, interval variable</p></li><li><p>d) Quantitative, interval variable</p></li></ul></li></ul><div data-type="horizontalRule"><hr></div><h3 collapsed="false" seolevelmigrated="true">Chapter 2: Descriptive Statistics</h3><ul><li><p>Overview of summarizing data effectively.</p></li></ul><h4 collapsed="false" seolevelmigrated="true">2.1 - Summarizing Data for a Categorical Variable</h4><ul><li><p><strong>Ways to summarize categorical data:</strong></p><ul><li><p>Frequency Distribution</p></li><li><p>Relative Frequency Distribution</p></li><li><p>Percent Frequency Distribution</p></li><li><p>Graphical representations: Bar charts and pie charts</p></li></ul></li></ul><h5 collapsed="false" seolevelmigrated="true">Frequency Distribution</h5><ul><li><p><strong>Definition:</strong> A tabular summary showing the number (frequency) of observations in each non-overlapping category.</p></li><li><p><em>Example:</em> Quality ratings for Marada Inn's accommodations.</p><ul><li><p>Poor: 2</p></li><li><p>Below Average: 3</p></li><li><p>Average: 5</p></li><li><p>Above Average: 9</p></li><li><p>Excellent: 1</p></li></ul></li></ul><h5 collapsed="false" seolevelmigrated="true">Relative and Percent Frequency Distributions</h5><ul><li><p><strong>Calculations:</strong></p><ul><li><p>Relative Frequency = (Frequency / Total Number of Observations)</p></li><li><p>Percent Frequency = Relative Frequency * 100</p></li></ul></li><li><p><em>Example:</em> [ \text{Relative Frequency for Poor} = 2/20 = 0.1 \text{ (10%)} ]</p></li></ul><h5 collapsed="false" seolevelmigrated="true">Bar Charts</h5><ul><li><p><strong>Description:</strong> Graphical display of qualitative data, with bars representing each category.</p></li><li><p>Characteristics: Bars have equal width and are separated.</p></li></ul><h5 collapsed="false" seolevelmigrated="true">Pie Charts</h5><ul><li><p><strong>Description:</strong> Circular chart divided into sectors representing relative frequencies.</p></li><li><p><strong>Example Calculation:</strong> For a relative frequency of 0.25, the angle in the pie chart = 0.25 * 360° = 90°.</p></li></ul><div data-type="horizontalRule"><hr></div><h4 collapsed="false" seolevelmigrated="true">2.2 - Summarizing Data for a Quantitative Variable</h4><ul><li><p><strong>Methods Include:</strong></p><ul><li><p>Frequency Distribution</p></li><li><p>Relative Frequency and Percent Frequency Distributions</p></li><li><p>Dot Plots</p></li><li><p>Histograms</p></li><li><p>Cumulative Distributions</p></li></ul></li></ul><h5 collapsed="false" seolevelmigrated="true">Frequency Distribution Example: Hudson Auto</h5><ul><li><p>Analyze the costs of parts used from 50 customer invoices.</p></li></ul><h5 collapsed="false" seolevelmigrated="true">Cumulative Distributions</h5><ul><li><p><strong>Types:</strong></p><ul><li><p>Cumulative Frequency</p></li><li><p>Cumulative Relative Frequency</p></li><li><p>Cumulative Percent Frequency

Cumulative Frequency

Definition: The cumulative frequency is the sum of the frequencies for all classes up to and including the current class.

Calculation Example: If you have the following frequency distribution:

• Poor: 2

• Below Average: 3

• Average: 5

• Above Average: 9

• Excellent: 1

The cumulative frequency would be:

• Poor: 2

• Below Average: 2 + 3 = 5

• Average: 5 + 5 = 10

• Above Average: 10 + 9 = 19

• Excellent: 19 + 1 = 20

Cumulative Relative Frequency

Definition: The cumulative relative frequency is the cumulative frequency divided by the total number of observations, which shows the proportion of observations at or below a certain level.

Calculation Example:Using the cumulative frequency from above:Total observations = 20

• Poor: 2/20 = 0.1

• Below Average: 5/20 = 0.25

• Average: 10/20 = 0.5

• Above Average: 19/20 = 0.95

• Excellent: 20/20 = 1.0

Cumulative Percent Frequency

Definition: The cumulative percent frequency is the cumulative relative frequency multiplied by 100 to express it as a percentage.

Calculation Example:Continuing from cumulative relative frequency:

• Poor: 0.1 * 100 = 10%

• Below Average: 0.25 * 100 = 25%

• Average: 0.5 * 100 = 50%

• Above Average: 0.95 * 100 = 95%

• Excellent: 1.0 * 100 = 100%

This way, you can summarize the data to understand how many observations fall below specific categories in both relative and percentage terms.</p></li></ul></li></ul><div data-type="horizontalRule"><hr></div><h4 collapsed="false" seolevelmigrated="true">2.3 - Summarizing Data for Two Variables Using Tables</h4><ul><li><p><strong>Concept:</strong> Methods used to analyze relationships between two variables.</p></li><li><p><strong>Crosstabulation:</strong> Summarizes data for two variables, useful for providing insight into relationships.</p></li></ul><div data-type="horizontalRule"><hr></div><h4 collapsed="false" seolevelmigrated="true">2.4 - Summarizing Data for Two Variables Using Graphical Displays</h4><ul><li><p><strong>Importance:</strong> Graphical displays can highlight patterns and trends more effectively than tables.</p></li><li><p><strong>Scatter Diagrams:</strong> Show the relationship between two quantitative variables.</p></li><li><p><strong>Trendlines:</strong> Provide an approximation of the relationship between variables.</p></li></ul><h5 collapsed="false" seolevelmigrated="true">Example: Panthers Football Team</h5><ul><li><p>Investigating relationship between interceptions made and points scored:</p><ul><li><p>Recognizes a positive correlation between higher interceptions and higher points.</p></li></ul></li></ul><div data-type="horizontalRule"><hr></div><h4 collapsed="false" seolevelmigrated="true">Graphical Displays</h4><ul><li><p><strong>Side-by-Side Bar Charts:</strong> Depict multiple bar charts demonstrating relationships between two variables without overlapping.</p></li><li><p><strong>Stacked Bar Charts:</strong> Each bar consists of segments representing different categories, allowing for percentage comparisons.</p></li></ul><div data-type="horizontalRule"><hr></div><h3 collapsed="false" seolevelmigrated="true">Conclusion</h3><ul><li><p>Understanding and visualizing data through various statistical methods enhances comprehension of economic trends and relationships.</p></li></ul><p></p>