Intro to Stats
Semester I Exam Review
Name
Chapter 1
The following list contains the ages of the people in an apartment complex.
35
50
11
10
18
17
14
22
65
24
23
10
20
52
62
6
55
12
9
15
5
23
9
16
48
12
33
14
19
26
1.
Draw a stemplot (see right) of the data. Find the mean and median.
2.
Draw a histogram of the data.
3.
Determine if there are any outliers mathematically.
4.
Describe the shape, center and spread of the histogram.
5.
Determine if each is categorical or quantitative:
a)
hours worked per week
b)
hair color
c)
favorite dessert
d)
height in cm
0
1
2
3
4
5
6
6.
What is a frequency histogram? How is it different than a relative frequency histogram?
7.
What types of graphs are appropriate for categorical data? For numerical data?
Mean SAT Verbal and Math Scores by State - 1990 through 2004
Participation Rate 2004
Mean SAT I Verbal
Mean SAT I Math
New York
Connecticut
87%
85%
497
515
510
515
Massachusetts
New Jersey
85%
83%
518
501
523
514
New Hampshire
D.C.
80%
77%
522
489
521
476
Maine
Pennsylvania
76%
74%
505
501
501
502
Delaware
Georgia
73%
73%
500
494
499
493
STATE
8. Find the five number summary, range and IQR of the Mean SAT I Math Scores above.
9. Find the standard deviation and variance of the Mean SAT I Math Scores above.(Use your calculator!)
10. Create a box plot of the data, labeling the number line and the 5 number summary.
11. The standard deviation of a data set is 3.2. What is the variance?
12. The variance of a data set is 3.2. What is the standard deviation?
13. The mean of a group of students on the ACT is 22.
a. Sam has a deviation from the mean of – 6. What is her ACT score?
b. Tim has a deviation from the mean of 8. What is his ACT score?
Chapter 2
14. The average running time of a movie is 115 minutes with a standard deviation of 6 minutes.
a)
What time is 2 standard deviations above the mean?
b)
What time is 1 standard deviation below the mean?
c)
What values are 3 standard deviations from the mean?
15. Kyle, Bob and James were each bragging that they were in better shape than the other two men. Kyle’s
weight is at the 95th percentile of men his height, while Bob is at the 75th percentile and James is at the 55th
percentile. Who is in the best shape? Explain your answer using mathematics.
17.
Go back to the SAT I Math Scores on page 1. What is the z-score for New Hampshire? What is
the z-score for Georgia? What does this tell you about the two scores?
18.
What Math score is at the 20th percentile?
19.
What percentile is a Math score of 515?
20.
Sam, Mariel, and Simone took the AP stats test, the AP Biology test, and the AP History test respectively.
Sam scored a 79, Mariel scored an 83, and Simone scored an 85. The national means and standard
deviations for the tests are:
AP Stats: x  75,   8.3 , AP Biology : x  75,   4.6 , AP History: x  80,   6.4
Who scored the best on their test in comparison to the others? Explain your math reasoning behind your answer.
21.
The following is a list of test scores on the last test:
42
64
72
a)
Find the  of the scores.
b)
Find the  of the scores.
c)
A score of 77 is at what percentile?
d)
What score is at the 60th percentile?
75
76
77
78
79
81
82
84
85
88
91
98
22.
Draw and label a normal curve with a mean = 220 and a standard deviation of 18. Also label the percentages
given by the Empirical Rule.
23. Use the above graph to answer the following questions. Do not use the table.
a)
What score is at the 50th percentile?
b)
What percent of scores are below 256?
c)
What percent of scores are between 202 and 238?
d)
What score is 2.5% of the scores above?
Use the table to answer e-g. Continue using the normal curve you drew above.
e)
What score is 28% of the scores below?
f)
What percent of scores is above 210?
g)
What percent of scores are between 200 and 240?
Use Table A to answer 24-25.
24.
Find the percent of values below z = -1.15.
25. What z-score has 24% of the values above it?