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STAT 110 - Section 5 Lecture 12

In this lecture from Spring 2012 at the University of South Carolina, Professor Hao Wang discusses the principles of good data presentation in statistics. Key concepts include the importance of random sampling and comparative experiments, how to structure effective data tables, and the different types of variables—categorical and quantitative. Additionally, he explores visual representations such as pie charts, bar graphs, line graphs, and the significance of proper labeling and clarity in conveying data insights.

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STAT 110 - Section 5 Lecture 12

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  1. STAT 110 - Section 5 Lecture 12 Professor Hao Wang University of South Carolina Spring 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. Roadmap • Statistics deals with data. • We know how to get good data. • - random sampling  • - randomized comparative experiments  • So, what’s the best way to present data?

  3. Data Tables Eye Color of 46 Students Eye Color # of persons percent Brown 18 39% Blue 17 37% Green 6 13% Hazel 4 9% Other 1 2% Total 46 100%

  4. Data Tables • What makes a good data table? • - labels • - units • - source • Tables typically summarize data. • But do they tell the whole story?

  5. Types of Variables categorical variable – places an individual into one of several groups or categories Example: Gender, college attended, field of study quantitative variable – takes numerical values for which arithmetic operations make sense operations: adding, averaging, etc. Example: Height, income, GPA, stock price, length

  6. Eye Color of 46 Students Eye Color # of persons percent Brown 18 39% Blue 17 37% Green 6 13% Hazel 4 9% Other 1 2% Total 46 100% What kind of variable is eye color? A – Categorical B - Quantitative

  7. Eye Color of 46 Students Eye Color # of persons percent 1 18 39% 2 17 37% 3 6 13% 4 4 9% 5 1 2% Total 46 100% What kind of variable is eye color? A – Categorical B - Quantitative

  8. Definitions frequency – the number of times a value occurs in the data relative frequency – for a value, the proportion (fraction or percent) of all observations that have that value

  9. Eye Color of 46 Students Eye Color # of persons percent Brown 18 39% Blue 17 37% Green 6 13% Hazel 4 9% Other 1 2% Total 46 100% Which column is the frequency? A – Eye Color B - # persons C - percent

  10. Pie Charts Pie Chart of the Eye Color Data

  11. Pie Charts • shows how a whole is divided into parts • How do you make a pie chart? • (1) draw a circle - this represents the whole • (2) draw wedges in proportion to the size of each part - each wedge represents each part • angles are harder to compare than lengths. • not a good way to compare sizes of the parts

  12. http://www.usgovernmentspending.com/us_budget_pie_chart

  13. http://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_charthttp://blogs.oracle.com/experience/entry/countdown_of_top_10_reasons_to_never_ever_use_a_pie_chart http://anametrix.com/index.php/easyblog/entry/pie-charts-are-everywhere-and-they-are-awful

  14. Bar Graphs • height of each bar shows rate or count • easier to draw than a pie chart • Called a “Frequency Bar Graph” when counts are used • Called a “Relative Frequency Bar Graph” when percentages are used

  15. Relative Frequency Bar Graph

  16. Frequency Bar Graph

  17. Which of the values can not be used on the vertical axis of a Relative Frequency Bar Chart? • A. 0 • B. 0.25 • C. 50% • D. 150

  18. Pictogram • Typically more interesting than a bar graph because it uses pictures in place of the bars.

  19. Be careful about pictogram Plus: Can be more visually appealing than a bar graph Minus: Can be misleading because our eyes respond to total area, not just height

  20. Line Graph: Average Price for Regular Unleaded Gasoline (Bureau of Labor Statistics)

  21. Line Graph • To display change over time, make a line graph. This can be used to display a quantitative variable changing over time. A line graph of a variable plots each observation against the time at which it was measured. • Time always goes on the horizontal scale. • Variable you’re measuring always goes on the vertical scale. • Connect the data points by lines to display the change over time.

  22. Average Unemployment Rate Blue = High School GradsPink = College Grads

  23. What should we look for? • Overall pattern. • A trend is a long-term upward or downward movement over time. • Striking deviations. • Seasonal variation. • A pattern that repeats itself at known regular intervals of time is called seasonal variation. • Many series of regular measurements over time are seasonally adjusted.

  24. Making Good Graphs • Use good labels and legends. • - variables, units, source • Make the data stand out! • - Drawing a graph isn’t a creative art project. • Pay attention to what the eye sees. • - Avoid pictograms and fancy 3D effects. • Watch the scales.

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