MATH 6350

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

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### 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)
• 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. ???
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
Content Goals
• Graphical Measures
• Numerical
• Stem-and-Leaf
• Histogram
• Boxplot
• Scatterplot
• Categorical
• Bar chart & pie chart
Stem-and-Leaf Plot
• Use Stem-and-Leaf to help
• Organize larger data sets
• Show the basic shape of the distribution
• Example: Test Scores
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

Stem-and-Leaf Plot
• How would you describe the distribution?
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
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
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
• 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?
Boxplot: A 5 Number Summary
• Example: Test Score Data

Q1

Med

Q3

Min

Max

Boxplots
• Usefulness
• Determine if there are possible “unusual” observations

Add a test score of 13 to the original data for Test Scores

*

Boxplots
• Usefulness
• Comparing distributions
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 = ____________
Measures of Spread of Data
• Range = ______________

1

5

7

14

6

Categorical Data

Same Example: Test Scores

Reorganize the Data into Categories

Categorical Graphs
• Pie Charts & Bar Charts
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)
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

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