1. Analyzing Categorical Data & Displaying Quantitative Data
Section 1.1 & 1.2
Reference Text:
The Practice of Statistics, Fourth Edition.
Starnes, Yates, Moore
Lesson 1.1.1

2. Starter Problem
Antoinette plays a lot of golf. This summer she got a new driver and kept track of how far she hit her tee shots in several rounds. Look at these data (drive lengths in yards) and then write a few sentences that describe the lengths of her drives:
246
260
230
233
254
203
223
193
238
220
210
237
270
240
192
204
250
274
235
222
225
241
200
226
Lesson 1.1.1

3. Today’s Objectives Analyze pie charts and bar graphs Two way tables:
Marginal Distribution
Conditional Distribution
A Titanic Disaster
Analyze Dot Plots
Describe CUSS  your new best friend
Stem and Leaf Plots: single, and back to back
Histograms
Lesson 1.1.1

4. Types of Variables
Categorical variables record which group or category an individual belongs to.
What color is your hair?
What year are you in school?
What city do you live in?
Did the tee shot land in the fairway?
It does NOT make sense to average the results.
Quantitative variables take on numeric values.
How tall is a person?
What score did a person get on the SAT?
How many desks are in a room?
How long was the tee shot?
It DOES make sense to average the results.
Lesson 1.1.1

5. Visual Representation of Categorical Variables
Categorical variables are typically represented by pie charts (for percents) or bar charts (percents or counts).
Married?
Count (M)
Percent
Single
41.8
22.6
Married
113.3
61.1
Widowed
13.9
7.5
Divorced
16.3
8.8
Lesson 1.1.1

6. Dilbert comics
Use a pie chart only when you want to emphasize each category’s relation to the whole. Pie charts are awkward to make by hand, but technology will do the job for you.

7. What Makes a Good Bar Graph?
All bars have the same width
X & Y axis’ labeled
Units
Title of Graph
Bad
Bars have different widths
Pictures replacing the bars (see example next slide)
No labels

8. Why Is This A Bad Bar Graph?
This ad for DIRECTV has multiple problems. How many can you point out?

9. Two Way Tables
Two – way tables are a visual representation of the possible relationships between two set of categorical data. The categories are labeled at the top and the left side of the table, with the frequency info appearing in the interior cells of the table. The “totals” of each row appear at the right, and the “totals” of each column appear at the bottom.

10. “If you could have a new vehicle, would you want a sport utility vehicle or a sports car?
Entries in the body of the table are called joint frequencies. The cells that contain the sum are called marginal frequencies.

12. Probability
When looking at a relative frequency table the percent or ratio is also the probability of that event happening over the ENTIRE TOTAL.
If a random selection was made, What's the probability a male selects an SUV?
21/240
If a random selection was made, What's the probability a female selects an SUV?
135/240
If a random selection was made, What's the probability that a SUV is selected?
156/240

13. Probability
Notice how all the probabilities have a denominator of 240! Its out of the entire table total!
Moral of the story… When asked for a probability that does not have a preexisting condition… look for the specific characteristics desired in the table divided by the table total.
P Event A = number of outcomes corresponding to event A 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒
Or you can look at it this way…
P specific charac𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 = Specific characteristics table total

14. Conditional probability
When we are calculating the probability of an event occurring given that another event has occurred, we are describing conditional probability.
Certain conditions have been preselected, and now we much calculate the probability based on that condition already happening.
When we have conditional probability our denominator value becomes the column total or the row total depending on which condition is given.
Example:
What is the probability of selecting
a sports car given a male?
V.S.
What's the probability a male
selects an SUV?

15. Conditional Probability
What if we knew one of the variables already? What is the probability that it’s a sports car GIVEN that it’s a male? Then our probability changes!!
𝑃( 𝑆𝑝𝑜𝑟𝑡𝑠 𝐶𝑎𝑟 𝑀𝑎𝑙𝑒 = Probability( sports car given that it’s a male) = =.65=65%

16. Comparing Two Different Questions
What is the probability of selecting a sports car given a male?
What's the probability a male selects an sports car?
𝑃(male selecting a sports car)= =0.1625=16.25%
𝑃( 𝑆𝑝𝑜𝑟𝑡𝑠 𝐶𝑎𝑟 𝑀𝑎𝑙𝑒 = =.65=65%

17. Flashback! Titanic Disaster
On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table below
Survival Status
Class of Travel
Survived
Died
Total
First Class
201
123
Second Class
118
166
Third Class
181
528

18. Conditional Probability
𝑃 𝑆𝑢𝑟𝑣𝑖𝑣𝑒𝑑 1𝑠𝑡 𝑐𝑙𝑎𝑠𝑠
201/324
𝑃 𝐷𝑖𝑒𝑑 3𝑟𝑑 𝑐𝑙𝑎𝑠𝑠
528/709
𝑃 1𝑠𝑡 𝑐𝑙𝑎𝑠𝑠 𝑠𝑢𝑟𝑣𝑖𝑣𝑒𝑑
201/500
P(survived)
500/1317
1) What is the percent of people who survived?
Is this a marginal or conditional
2) Given the passenger survived, what are the percentages for each class?
Survival Status
Class of Travel
Survived
Died
Total
First Class
201
123
324
Second Class
118
166
284
Third Class
181
528
709
500
817
1317

19. Break!
- 5 Minutes

20. Section 1.2: Quantitative Data w/ Graphs
Dot plots
C.U.S.S
Histograms
Stem plots

21. Types of Variables
Categorical variables record which group or category an individual belongs to.
What color is your hair?
What year are you in school?
What city do you live in?
Did the tee shot land in the fairway?
It does NOT make sense to average the results.
Quantitative variables take on numeric values.
How tall is a person?
What score did a person get on the SAT?
How many desks are in a room?
How long was the tee shot?
It DOES make sense to average the results.
Lesson 1.1.1

22. Visual representation of Quantitative Variables: Dotplots
The most basic method is a dotplot.
Every data point can be seen on the plot.
Construction method:
Draw a horizontal axis with a scale that covers the full range of values for the variable.
Put a dot on (or above) the axis for each data point.
If data duplicate, stack them vertically.
Construct a dotplot now of Antoinette’s drives:
246
260
230
233
254
203
223
193
238
220
210
237
270
240
192
204
250
274
235
222
225
241
200
226
Lesson 1.1.1

23. Dotplot of Drive Data Based on the dotplot, estimate the center.
We see it around 230 or 240 yards.
Any Unusual Data Points.
No outliers present
Estimate the spread.
Roughly from 190 to almost 280, so spread is about 90 yards.
Describe the shape.
It appears “mound-shaped” with most of the data clustered at the center and with tails at each end.
Lesson 1.1.1

24. C.U.S.S
C: Center
Median, where is it?
Mean can also describe the center, but is not resistant…
U: Unusual data points
Outliers! Are there any? We can calculate them…later in 1.3
S: Spread
Describe the variability of the graph
(largest value – smallest value)
S: Shape
How many peaks? Is the data clumped in a general location? Is data stretching to the right (skewed right). Is the data stretching to the left (skewed left).
LASTLY…Always, ALWAYS C.U.S.S it out when describing graphs of data

25. Histograms Another important method is a histogram.
Individual data points cannot be seen on the plot.
Many data points are grouped together in vertical bars.
Construction method:
Draw a horizontal axis with a scale that covers the full range of values for the variable.
Decide bar width (also called class width) so that 5 to 10 bars will cover the full range of data.
Set borders for bars, count frequencies, draw bars.
Use a vertical axis to show the bar height.
Lesson 1.1.1

26. Histogram of Drive Data
From a visual examination, estimate the center, unusual points, spread and the shape. (CUSS)
As before, you should see the center around 230 to 240, no unusual points, the spread looks like 90, and the shape still looks like a mound.
Lesson 1.1.1

27. Stemplots AKA: Stem & Leaf Plots
One way to organize numerical data is to make a stemplot.
Lets turn to the board and walk through how to make a stemplot of the following data, found on pg 33

28. DATA

29. Stemplots check list Did we make a stemplot?
Did we talk about splitting stems
…  upper and lower bounds
Did we talk about back to back stemplots?
KEY?
Good…now we can move on 

30. Percent of Population Over 65 by State4 9 5 6 7 8 10 2 11 1 3 12 13 14 15 16 17 18
Note: 4|9 = 4.9%
Lesson 1.1.2

31. Today’s Objectives Analyze pie charts and bar graphs Two way tables:
Marginal Distribution
Conditional Distribution
A Titanic Disaster
Analyze Dot Plots
Describe CUSS  your new best friend
Stem and Leaf Plots: single, and back to back
Histograms
California Standard 14.0
Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
Lesson 1.1.1

32. Start Chapter 1 reading guide Due: Day of Chapter 1 Test (TBA)
Homework
Start Chapter 1 reading guide Due: Day of Chapter 1 Test (TBA)
1.1 Homework Worksheet
1.2 homework Worksheet
Lesson 1.1.1