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MATH 6350

MATH 6350 Ginger Holmes Rowell, Ph. D. Probability & Statistics Are All Around Us Tell us what you found (from the homework) Probability Statistics Probability & Statistics in the Curriculum Homework (send paragraph by email)

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MATH 6350

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  1. MATH 6350 Ginger Holmes Rowell, Ph. D.

  2. Probability & Statistics Are All Around Us • Tell us what you found (from the homework) • Probability • Statistics

  3. Probability & Statistics in the Curriculum • Homework (send paragraph by email) • Examine the NCTM standards for Probability and Statistics from K-12. • Write a paragraph about your thoughts on these standards • Do you agree, is it realistic, is it really happening, how will you make it happen, and etc. ???

  4. Content Goals • Numerical Measures of Center • Mean, Median, Mode • Numerical Measures of Spread • Range, standard deviation, variance • Numerical Measures of Location • Percentiles (quartiles), z-scores

  5. Content Goals • Graphical Measures • Numerical • Stem-and-Leaf • Histogram • Boxplot • Scatterplot • Categorical • Bar chart & pie chart

  6. Stem-and-Leaf Plot • Use Stem-and-Leaf to help • Organize larger data sets • Show the basic shape of the distribution • Example: Test Scores

  7. Stem-and-Leaf Plot • Data: Test Scores (out of 100 pts) 99, 54, 61, 100, 98, 62, 72, 80, 93, 65, 75, 75, 81, 89, 82, 97, 100, 69, 76, 89, 84, 89, 88, 98, 87, 84, 87, 62 79, 84, 79, 81, 84

  8. Stem-and-Leaf Plot • How would you describe the distribution?

  9. Histogram • Can have a frequency, relative frequency or a density histogram • Use density if it is not realistic to make the bars the same width • Example: Test Scores

  10. Axes labeled Columns the same width Midpoints labeled Can you tell me how the endpoints work? What is the max score? Where does a score of 80 go? Frequency Histogram

  11. Just adjust the vertical axis to Percent Percent Histogram

  12. Same data can be represented differently A Weakness of Histograms

  13. Homework (not for a grade) • Go to the Bin Width Histogram Applet by Webster West • URL: • Play with the histogram to better see this phenomenon • Write a couple of sentences explaining what you learned from using this applet

  14. Share Your Survey • How many siblings? __ Brothers # ___ Sisters # ___ • How often do you watch tv (hours per day)? • How much time should you spend on math homework? • How much time do you spend on math homework? • Where do you plan to go to college? • Where do you live? How many miles do you drive to school? • Name your favorite color, food, singer, store. • What types of video games do you like (sports, adventure, fantasy, racing). • How much time do you spend playing video games?

  15. Boxplot: A 5 Number Summary • Example: Test Score Data Q1 Med Q3 Min Max

  16. Boxplots • Usefulness • Determine if there are possible “unusual” observations Add a test score of 13 to the original data for Test Scores *

  17. Boxplots • Usefulness • Comparing distributions

  18. How Do You Find Quartiles • Quartiles • Q1=Lower Quartile=QL=25th Percentile • Find the Median of the Lower Quartile (good estimate) • Q3=Upper Quartile=QU=75th Percentile • Find the Median of the Upper Quartile (good estimate) • Interpretation = ____________

  19. Measures of Spread of Data • Range = ______________

  20. 1 5 7 14 6 Categorical Data Same Example: Test Scores Reorganize the Data into Categories

  21. Categorical Graphs • Pie Charts & Bar Charts

  22. Homework (Hand-in) • Hand-in Assignment 2 • Due Wednesday, August 27th • Complete the Pie Chart and Bar Chart Using Excel Handouts • Email the file(s) with the “Fancy Graph” to me. (rowell@mtsu.edu)

  23. Measure of Spread from the Mean • Variance (from the mean) • Example with easy numbers -1, -1, 0, 1, 1 Will work with this on the white board

  24. Content Goals • Numerical Measures of Center • Mean, Median, Mode • Numerical Measures of Spread • Range, standard deviation, variance • Numerical Measures of Location • Percentiles (quartiles), z-scores

  25. Content Goals • Graphical Measures • Numerical • Stem-and-Leaf • Histogram • Boxplot • Scatterplot • Categorical • Bar chart & pie chart

  26. Homework (not for grade) • Find the sample standard deviation of the number of siblings that the “hypothetical” students have • Use a sentence to interpret this value in the context of the problem

  27. Homework Review • NCTM Standards Paragraph (not for grade) • Histogram Applet (not for grade) • Excel Pie and Bar Charts (Hand-in for a Grade) • Find the standard deviation of the number of siblings a “student” has.

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