Wednesday, August 11 (131 minutes)
Wednesday, August 27: 1.1 Analyzing Categorical Data
Read 2–4
What’s the difference between categorical and quantitative variables?
Focus on “who is being measured” and “what is being measured”
Do we ever use numbers to describe the values of a categorical variable? Do we ever divide the distribution of a quantitative variable into categories?
Make sure to discuss categorical variables that are recorded with numbers (p3). For example, AIMS results, AP scores, area codes.
Also, often variables like age, weight, and so on are divided into categories and treated as a categorical variable.
What is a distribution?
Note the “values” can be words or numbers
Alternate Example: US Census Data
Here is information about 10 randomly selected US residents from the 2000 census.
|State |Number of|Age |Gender |Marital |Total |
| |Family | | |Status |Income |
| |Members | | | | |
|Atlanta Hawks |98.0 |Houston Rockets |106.0 |Oklahoma City Thunder |105.7 |
|Boston Celtics |96.5 |Indiana Pacers |94.7 |Orlando Magic |94.1 |
|Brooklyn Nets |96.9 |Los Angeles Clippers |101.1 |Philadelphia 76ers |93.2 |
|Charlotte Bobcats |93.4 |Los Angeles Lakers |102.2 |Phoenix Suns |95.2 |
|Chicago Bulls |93.2 |Memphis Grizzlies |93.4 |Portland Trail Blazers |97.5 |
|Cleveland Cavaliers |96.5 |Miami Heat |102.9 |Sacramento Kings |100.2 |
|Dallas Mavericks |101.1 |Milwaukee Bucks |98.9 |San Antonio Spurs |103.0 |
|Denver Nuggets |106.1 |Minnesota Timberwolves |95.7 |Toronto Raptors |97.2 |
|Detroit Pistons |94.9 |New Orleans Hornets |94.1 |Utah Jazz |98.0 |
|Golden State Warriors |101.2 |New York Knicks |100.0 |Washington Wizards |93.2 |
Suggest that students mentally populate a histogram with dots to make them less abstract.
______________________________________________________________________________
Read 33–36
How do you make a histogram?
Emphasize labels, equal class widths, what to do with boundary values…
Read 38–41
Why would we prefer a relative frequency histogram to a frequency histogram?
Ex: comparing distribution of GPA for our class and the entire school.
What will cause you to lose points on tests and projects (and turn the rest of Mr. Tabor’s hair gray)?
Making a “histogram” with observation number on the x axis and value of the variable on the y axis. Very common mistake when using Excel.
HW #14: page 43 (51, 53, 55, 59–62)
Thursday, September 4: 1.3 Describing Quantitative Data with Numbers
Read 48–50 Distribute formula sheets
What is the difference between [pic] and [pic]?
Give an example of using [pic] to estimate [pic].
What is a resistant measure? Is the mean a resistant measure of center?
How can you estimate the mean of a histogram or dotplot?
Give a simple dotplot and show how deviations from mean add to 0: 1, 2, 3, 6, 8
Read 51–53
Is the median a resistant measure of center? Explain.
Mean and Median Applet at TPS site
How does the shape of a distribution affect the relationship between the mean and the median?
Home prices, etc.
Read 53–55 After first paragraph, sketch dotplots to illustrate this situation.
What is the range? Is it a resistant measure of spread? Explain.
What are quartiles? How do you find them?
Draw generic dotplot with 12 dots. Label quartiles and then label range and IQR.
What is the interquartile range (IQR)? Is the IQR a resistant measure of spread?
|Sandwich |Fat (g) |
|Filet-O-Fish® |19 |
|McChicken® |16 |
|Premium Crispy Chicken Classic Sandwich |22 |
|Premium Crispy Chicken Club Sandwich |33 |
|Premium Crispy Chicken Ranch Sandwich |27 |
|Premium Grilled Chicken Classic Sandwich |9 |
|Premium Grilled Chicken Club Sandwich |20 |
|Premium Grilled Chicken Ranch Sandwich |14 |
|Southern Style Crispy Chicken Sandwich |19 |
Alternate Example: McDonald’s Fish and Chicken Sandwiches
Here are data on the amount of fat (in grams) in 9 different McDonald’s fish and chicken sandwiches. Calculate the median and the IQR.
Read 56–57 (read long teaching tip on page 56)
What is an outlier? How do you identify them? Are there outliers in the chicken/fish sandwich distribution?
IQR dance =)
|Sandwich |Fat |
|Big Mac® |29 |
|Cheeseburger |12 |
|Daily Double |24 |
|Double Cheeseburger |23 |
|Double Quarter Pounder® with cheese |43 |
|Hamburger |9 |
|McDouble |19 |
|McRib® |26 |
|Quarter Pounder® Bacon and Cheese |29 |
|Quarter Pounder® Bacon Habanero Ranch |31 |
|Quarter Pounder® Deluxe |27 |
|Quarter Pounder® with Cheese |26 |
Here is data for the amount of fat (in grams) for McDonald’s beef sandwiches. Are there any outliers in this distribution?
Read 57–59
What is the five-number summary? How is it displayed?
Draw parallel boxplots for the beef and chicken/fish sandwich data. Compare these distributions.
• Discuss common errors: using “IQR” to describe the region, not the distance between quartiles, can’t see the peaks when using a boxplot (show presidential days in office file).
• Talk about how to make boxplots on TI—see page 59, mention VIDEOS!
HW #15: page 47 (69–74), page 69 (79, 81, 83, 85, 86, 88, 89, 91, 93, 94a)
Monday, September 8: 1.3 Standard Deviation
In the distribution below, how far are the values from the mean, on average?
[pic]
What does the standard deviation measure?
Use dotplot summaries applet at to practice estimating SD
Do some guesses that are clearly too small and too big and get kids to explain how they know the guesses are too small or too big.
What are some similarities and differences between the range, IQR, and standard deviation?
Sim: all measure variability
Diff: resistance to outliers, using all the data
Do the by-hand SD calculation for dotplot above before doing the reading!
Read 60–62
How is the standard deviation calculated? What is the variance?
Remind them the formula is on the formula sheet
Don’t really need to know about variance now, just SD squared
Discuss why we use n – 1 if students are interested
What are some properties of the standard deviation?
Alternate Example: A random sample of 5 students was asked how many minutes they spent doing HW the previous night. Here are their responses (in minutes): 0, 25, 30, 60, 90. Calculate and interpret the standard deviation.
Read 63–66 Go through all the calculator stuff, including difference between s and [pic]
What factors should you consider when choosing summary statistics?
Discuss four-step process
HW #16: page 71 (97, 99, 101–105, 107–110)
Tuesday, September 9: FRAPPY! College fair?
FRAPPY page 74
HW #17: page 76 Chapter Review Exercises
Wednesday, September 10: Review Chapter 1
Matching Distributions activity from Activity Based Statistics
HW #18: page 78 Chapter 1 AP Statistics Practice Test
Friday, September 12: Chapter 1 Test
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