Warm-Up
• List all of the different types of graphs you can remember
from previous years:
Paper Airplanes
• Make your best paper airplane out of the printer paper provided
• Go out in the hall and fly it to your best ability and record how many
feet/squares it flies before coming to rest
• Do this 3 times
• Come back in and record your answer here:
• Also put your dot where it needs to go…(dotplot)
Section 1.1
Data Analysis: Categorical and Quantitative Data
Variables…
• An Individual is an object described by data from a data set.
(Can be people, animals, or objects).
• A Variable is any characteristic of an individual. A variable can
take different values for different individuals.
• A Categorical Variable places an individual into one of several
groups or categories.
• A Quantitative Variable takes numerical values for which it
makes sense to find an average.
Ways to display categorical data
• Bar Graphs
• Pie Charts
• Segmented Bar
Graph
To Display Variables
• The Distribution of a variable tells us what values the variable
takes and how often it takes these values.
• A Frequency Table (used for categorical variables) lists
individuals by a variable and how many individuals are within
the categories of that variable.
A
B
C
D
F
10
19
21
7
3
• A Relative Frequency Table is a frequency table that divides
each count by the total, making each value a percentage of
the whole.
A
10/60
B
19/60
C
21/60
D
7/60
F
3/60
Roundoff Error
• Roundoff Error is when percents or vales are rounded within a
relative frequency or frequency table (respectively) which
causes the total to not match what is expected.
• Ex: Student AP Scores In Millions
• Total: 10,531,277 students
1
2
3
4
5
1.7
2.1
3.8
2.3
.9
Marginal Distribution
• A Marginal Distribution is a distribution of one categorical
variable in a two-way table. As in, how the variable is
distributed among the total of the table.
• It is called a marginal distribution because it will literally use
the margin of the two-way table.
Left Handed
Right Handed
Males
1
15
Females
3
14
Conditional Distribution
• A Conditional Distribution of a variable describes the values
of the variable among individuals who have a specific value of
another variable. There is a separate conditional distribution
for each value of the other variable.
Left Handed
Right Handed
Males
1
15
Females
3
14
Example of Conditional Dist.
Young Adults by Gender and Chance of Getting Rich
Gender
Opinion
Female
Male
Total
Almost No Chance
96
98
194
Some Chance but
probably not
426
286
712
A 50-50 Chance
696
720
1416
A Good Chance
663
758
1421
Almost Certain
486
597
1083
Total
2367
2459
4826
Let’s do the conditional distribution for males…
Now females…
Your Answer…
Response
Female
Male
Almost No Chance
4.1%
4.0%
Some Chance but
probably not
18.0%
11.6%
A 50-50 Chance
29.4%
29.3%
A Good Chance
28.0%
30.8%
Almost Certain
20.5%
24.3%
• To compare these, we would use a side-by-side bar graph
Association
• We say there is an association between two variables if
specific values of one variable tend to occur in common with
specific values of the other.
• For example, if we surveyed all of the fall athletes there would
be an association between being male and playing football.
Simpson’s Paradox
• Simpson’s Paradox is when an association between two
variables that holds for each individual value of a third variable
can be reversed when the data for all values of the third
variable are combined.
• Example: Accident Victims and how they are transported
Helicopter
Road
Victim Died
64
260
Victim Survives
136
840
Total
200
1100
More information
Serious Accidents
Helicopter
Road
Died
48
60
Survived
52
40
Total
100
100
Less Serious Accidents
Helicopter
Road
Died
16
200
Survived
84
800
Total
100
1000
Homework
• Pg. 22 (9-12, 14-15, 17-22, 26)