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Algebra II & Trigonometry
Measures of Dispersion
A2.S.3
A2.S.4
Calculate measures of central tendency with group frequency distributions
Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation,
variance) for both samples and populations
1. If the range of a set of data is 40 and the highest score is 50, what is the lowest score?
(1) –10
(3) 10
(2) 1.2
(4) 90
2. If the variance of a set of data is 16, what is the standard deviation?
(1) 256
(3) 8
(2) 32
(4) 4
3. If the standard deviation of a set of data is 16, what is the variance?
(1) 256
(3) 8
(2) 32
(4) 4
4. Which of the following sets of data has the greatest range?
(1) {32, 65, 34, 43, 16}
(2) {14, 76, 56, 42, 86}
(3) {65, 54, 75, 45, 86}
(4) {21, 45, 90, 65, 54}
5. What is the variance for the following set of data: 4, 6, 8, 10, 12
(1) 1.682
(2) 2.828
(3) 8
(4) 64
6. What is the interquartile range of the following set of data:
22, 48, 18, 34, 59, 47, 16, 82, 11, 39
Show how you arrived at your result.
7. After giving a test to her class, Mrs. Statsrule decided to raise everyone’s score by 5 points. How does this affect the
standard deviation?
(1) increases it by 5 points
(2) increased it by 5 points
(3) there is no change
(4) the change cannot be determined
8. What is the sample standard deviation for the following set of data:
(1) 6.9
(2) 7.6
(3) 16.8
(4) 101
6, 12, 14, 19, 24, 26
9. What is the population standard deviation for the following set of data? 6, 12, 14, 19, 24, 26
(1) 6.9
(2) 7.6
(3) 16.8
(4) 101
10. The table below shows the temperature in various places in New York State on July 22, 2008.
Location
Temperature
Location
Albany
85
New York City
Binghamton
81
Niagara Falls
Buffalo
77
Oswego
Corning
81
Plattsburg
Dunkirk
75
Poughkeepsie
Elmira
81
Rochester
Geneva
79
Saranac lake
Glens Falls
81
Syracuse
Islip
85
Utica
Ithaca
81
Watertown
Kingston
85
White Plains
Massena
79
Yonkers
Temperature
89
77
77
80
85
79
75
81
81
77
89
89
(a) According to the data, to the nearest tenth, what was the mean temperature in New York State on July 22, 2008?
(b) If we use standard deviation as a measure of dispersion, would we find sample standard deviation or population
standard deviation in this case? Explain.
(c) What is the appropriate standard deviation of the temperatures, to the nearest tenth?
11. Both of the following sets of data have the same mean. Without doing any computation, determine which one has the
smaller standard deviation. Explain how you came to your conclusion.
A: 10, 90, 40, 5, 30, 5
B: 32, 30, 36, 28, 24, 30
12. The PSAT scores of a group of students in Kennedy High School are given in the table below.
Score
Frequency
Score
Frequency
Score
20
1
45
28
70
25
2
50
36
75
30
2
55
34
80
35
2
60
27
40
14
65
23
Frequency
11
3
2
(a) Based on the data given above, to the nearest hundredth, what is the mean PSAT score of these students?
(b) To the nearest hundredth, what is the sample standard deviation of the students in Kennedy High School?
13. The name, year of birth, and year of appointment for the 2008 Supreme Court justices are listed in the table below.
Name
John G. Roberts (Chief Justice)
Samuel A. Alito, Jr.
Stephen Breyer
Ruth Bader Ginsburg
Anthony M. Kennedy
Antonin Scalia
David Souter
John Paul Stevens
Clarence Thomas
Year of Birth
1955
1950
1938
1933
1936
1936
1939
1920
1948
Year of Appointment
2005
2006
1994
1993
1988
1986
1990
1975
1991
(a) Find, to the nearest tenth, the mean, median, and first and third quartiles of the number of years the Supreme Court
justices have served as of 2008.
(b) Find the range of their years of service and the interquartile range of their years of service as of 2008.
(c) What is the “average” age of a Supreme Court justice as of 2008? Explain why you chose the measure of central
tendency that you did.
14. The table below lists the ages of people who attended the Screaming Ghouls rock concert.
Age
12
13
14
15
16
17
18
Frequency
23
46
56
65
43
38
21
Age
19
20
21
22
23
31
42
(a) What is the mean age of the rock concert attendees, to the nearest hundredth?
(b) What is the standard deviation, to the nearest hundredth?
(c) Who would be interested in this type of information?
Frequency
11
10
6
3
2
2
1