Univariate Distributions
Overview
I. Exploring Data
Describing patterns and departures from
patterns (20%-30%)
Exploring analysis of data makes use of
graphical and numerical techniques to
study patterns and departures from
patterns. Emphasis should be placed on
interpreting information from graphical and
numerical displays and summaries.
I. Exploring Data
A. Constructing and interpreting graphical
displays of distributions of univariate data
(dotplot, stemplot, histogram, cumulative
frequency plot)
1.
2.
3.
4.
Center and spread
Clusters and gaps
Outliers and other unusual features
Shape
Multiple Choice Questions
• Read and think for one minute, and write your
answer.
• Discuss with group members for 30 seconds
and decide on a final answer.
• Discuss as a group for as long as we need to. . .
Source: AP Practice Exam
Answer: B
Source: AP Practice Exam
Answer: D
Source: 2001 AP Exam
I. Exploring Data
B. Summarizing distributions of univariate
data
1. Measuring center: median, mean
2. Measuring spread: range, interquartile
range, standard deviation
3. Measuring position: quartiles, percentiles,
standardized scores (z-scores)
4. Using boxplots
5. The effect of changing units on summary
measures
Source: 2007 AP Exam
Answer: C
Source: AP Course Description
Answer: B
Answer: E
Source: AP Practice Exam
Answer: C
Source: AP Practice Exam
Answer: E
Source: AP Practice Exam
Answer: A
Free Response Questions
• We’ll do each one a little differently, so listen
for directions.
• They’ll all start with you reading and
answering the question, but a bit faster than
you would need to do on the actual exam.
Source: AP Practice Exam
I. Exploring Data
C. Comparing distributions of univariate
data (dotplots, back-to-back stemplots,
parallel boxplots)
1. Comparing center and spread: within group,
between group variables
2. Comparing clusters and gaps
3. Comparing outliers and other unusual
features
4. Comparing shapes
Source: 1997 AP Exam
Answer: B
22. The back-to-back stem-and-leaf plot below gives the percentage of students who dropped out of
school at each of the 49 high schools in a large metropolitan school district.
School Year
1989-1990
9
4 4 4 4 4 3 3 2 2 2
9 9 9 7
4
School Year
1992-1993
9
2
7
2
9
1
6
2
8
9
1
6
2
8
8
1
6
1
8
8
1
6
0
7
7 6
0 4
7 0 5 6 6 6 7 7 7 8 8 8 9 9
0 1 0 0 0 0 1 1 1 1 2 2 2 3 3 4 4 4 4
5 1 5 5 5 6 6 6 6 7 7 7 7 8
0 2 1 3
6 2
2 3 0 1 1 2
6 3 5
4
For 1992-1993, 1|2 represents 12%.
Which of the following statements is NOT justified by these data?
(A) The drop-out rate decreased in each of the 49 high schools between the 1989-1990 and 19921993 school years.
(B) For the school years shown, most students in the 49 high schools did not drop out of high school.
(C) In general, drop-out rates decreased between the 1989-1990 and 1992-1993 school years.
(D) The median drop-out rate of the 49 high schools decreased between the 1989-1990 and 19921993 school years.
(E) The spread between the schools with the lowest drop-out rates and those with the highest dropout rates did not change much between the 1989-1990 and 1992-1993 school years.
Source: 1997 AP Exam
Answer: A
Source: 2006 AP Exam
Source: 2006 AP Exam
Source: 2006 AP Exam
Source: 2006 AP Exam
Source: 2006 AP Exam
Source: 2006 AP Exam
Source: 2011 AP Exam
Source: 2011 AP Exam
Source: 2011 AP Exam