1. Answer True or False. The main types of data are qualitative and numerical.
2. The two types of variables are discrete and ______.
3. The measurement scale for a ______ variable does have gaps.
4. In describing a data set of measurements, the computation of numerical measures is
irrelevant.
5. Both, categorical and numerical data can be described graphically using graphs and
______.
6. A frequency table for a sample of units
A) shows all sample units
B) shows the counts of individual categories
C) shows all units within a category
D) shows the relative frequencies of each category
7. A die is rolled 16 times, the scores are shown below.
6
1
4
1
1
2
6
4
2
6
5
3
3
6
5
2
a) Find the frequency of even numbers.
b) Find the relative frequency of even numbers. Round your answer to three decimal
places.
8. A die is rolled 16 times, the scores are shown below.
5
6
5
6
6
1
5
2
4
5
3
2
3
5
1
3
a) Find the frequency of 5.
b) Find the relative frequency of 5. Round your answer to four decimal places.
9. A die is rolled 16 times, the scores are shown below.
6
1
5
4
1
2
5
5
2
6
3
3
3
6
2
4
a) Find the frequency of numbers larger than 4.
b) Find the relative frequency of numbers larger than 4. Round your answer to four
decimal places.
Page 1
10. In 2007/2008 basketball season, Grant Hill scored 358 field goals, 33 3-point field goals,
and 170 free-throw goals. Find the pie chart that better describes the data.
A)
B)
C)
D)
Page 2
11. The following table shows the countries whose teams have won the UEFA Champions
League.
Country
Spain
England
Italy
Germany
Netherlands
Other
Frequency
12
11
11
6
6
8
a) Calculate the relative frequency of each country. Round your answers to three decimal
places
b) Select the pie chart that better describes the data.
I
II
III
Page 3
12. Find the histogram that better describes the data.
Value x
1
2
3
4
5
Total
I
Frequency
4
5
4
3
2
18
Relative Frequency
0.22
0.28
0.22
0.17
0.11
1.000
II
Page 4
III
13. The top number of goals scored by a national team in the last 18 FIFA's World Cups is
shown below. Select the dot diagram that matches with the data.
14
15
15
16
16
17
23
22
12
18
15
14
15
19
14
27
15
18
I
II
Page 5
14. The number of touchdowns of a college football team is:
38 36 29 33 37 34 35 34 43 27 36
31 22 28 36
a) Complete the frequency distribution.
Class Interval
21 - 24
25 - 28
29 - 32
33 - 36
37 - 40
41 - 44
Total
Frequency
---5
------3
1
20
38
21
26
26
27
Relative Frequency
---0.250
------0.150
0.050
1.000
b) Select the line diagram that matches the data.
I
II
III
15. The following data represents the Buccaneers number of touchdowns per season, in the
last 20 seasons. Make a stem-and-leaf display.
16. Use the stem-and-leaf display to construct a frequency distribution with intervals 10-12,
13-15, ..., 25-27.
1 4 8 5 1 5 4 6 5 6 9
3 6 0
2 3 7 2 0 5 3
7 8
Page 6
17. The table below shows the fastest race lap in the F1 Grand Prix in Monza.
Year
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
Speed (km/h)
246
237
252
253
256
257
255
249
245
244
Year
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
Speed (km/h)
243
244
248
241
240
243
250
242
243
242
Make a stem-and-leaf display with a 2-digit stem.
18. Calculate the mean and median of the following data set.
13,
14,
1,
11,
8
19. Calculate the mean and median of the following data set. Round your answer to the
nearest tenth.
31
28
A) 39.3 and 32, respectively
B) 39.3 and 34, respectively
34
56
32
55
C) 39.3 and 33, respectively
D) Mean: 39.3; there is no median
20. Calculate the mean and the median of the following data set.
4.8
4.5
3.8
3.7
4.8
5.4
Page 7
21. In a period of twelve years, the record low temperatures (F) in Morrow GA were:
Find the dot diagram that corresponds to these data.
I
II
III
22. Calculate the quartiles of the following data set.
17
22
22
17
23
22
22
17
23
17
10
17
17
22
23
17
23
23. Calculate the third quartile.
30
18
10
17
A) 20
19
17
18
23
B) 25
25
25
20
C) 19
21
23
30
19
25
10
10
25
D) 21
24. Answer True or False. The second quartile of a data set always corresponds to the median.
25. Answer True or False. The second quartile of a data set always corresponds to the mean.
26. Find the 80th percentile.
1.6
4.5
A) 7.5
1.7
1.8
1.8
1.9
2.1
2.5
3.0
3.0
4.4
4.5
5.9
7.1
7.4
7.5
B) 7.7
C) 7.52
D) 7.6
7.7
8.6
9.3
9.5
Page 8
27. Find the interquartile range.
128
154
124
251
194
252
129
156
217
157
210
254
163
211
172
76
102
28. Answer True or False. The interquartile range is the difference between any two
consecutive quartiles.
29. Answer True or False. The range is the difference between the largest observation and the
smallest observation.
30. For the data set
19
13
9
a) Calculate the deviations ( x  x ) . Round your answers to two decimal places.
b) Calculate the sample variance and the standard deviation.
31. For the data set
2
3.2
8.8
6.4
5.9
a) Calculate the deviations ( x  x ) and check to see that they add up to 0.
b) Calculate the sample variance and the standard deviation.
Round your answers to two decimal places.
32. For the data set
5
2
6
6
calculate s2 by using the alternative formula. Round your answer to the nearest tenth.
33. Find the variance of the following data set.
A) 1.4
B) 2.0
5
C) 1.7
8
8
D) 3.0
34. Find the standard deviation of the following data set.
A) 28.7
B) 29.7
290
305
C) 25.9
D) 24.9
Page 9
302
355
35. A football fan recorded the total number of points scored by 5 teams during week 1.
31
54
31
36
49
a) Calculate the sample variance.
b) Calculate the sample standard deviation.
36. eA report on the points gained by football teams playing at home in week 2 of the 2009
season are summarized below.
Descriptive Statistics:
Variable
N
PntHom
16
Variable
PntHom
PntHom
Mean
22.86
Minimum
3
Maximum
28
Median
23.50
StDev
11.95
Q1
13.50
Q3
24.00
a) Calculate the sample variance.
b) Calculate the interquartile range.
37. Answer True or False. According to the empirical guidelines for symmetric bell-shaped
distributions, approximately 68% of the data lie within x  s .
38. Refer to the data.
37
21
29
42
25
25
48
35
31
39
34
24
42
40
28
24
43
40
44
32
a) Calculate x and s.
b) Find the proportion of the observations that are in the intervals x  s , x  2s , and
x  3s .
Page 10
39. Based on the boxplot,
complete the table.
Minimum
----
Q1
----
Median
----
Page 11
Q3
----
Maximum
----
40. During the 2008-2009 regular season, the Orlando Magics won 59 games. The difference
of points in 24 of these games is shown below. Find the time plot that corresponds to these
data.
I
II
Page 12
41. During the 2008-2009 regular season, the Orlando magics won 59 games. The difference
of points in 24 of these games is shown below. Find the control chart that corresponds to
these data.
I
II
Page 13
42. The 2008 OPEC's Annual Statistical Bulletin reported that Ecuador's values of exports in
the period 1988-2008 (m $).
a) Select the time plot of the values of exports.
I
II
Page 14
III
b) How many points are out of the control area x  2s ?
Page 15
43. The stem-and-leaf display given here shows the final examination scores of students in a
statistics course. (Leaf unit = 1.0)
Stem-and-Leaf
Display of Scores
2
5 7
3
2 4 4
4
1 7 7 9
5
0 3 3 6
6
0 1 2 4
7
2 3 5 5
9 9
8
0 3 4 5
9
0 3 3 6
8
4 7
5 6 8
7
a) Find the median score.
b) Find the quartiles Q1 and Q3.
c) What proportion of the students scored below 70? Round your answer to three decimal
places.
44. Answer True or False. If M is the mean of x1, x2, and x3, then the mean of 10x1, 10x2, and
10x3 is 10M.
45. Answer True or False. If M is the mean of x1, x2, and x3, then the mean of x1 + 9, x2 + 9,
and x3 + 9 is M + 9.
46. Let s1, s2, and s3 be the standard deviations of the bell-shaped graphs I, II, and III,
respectively. Place them in increasing order.
A) s3 , s1 , s2
B) s2 , s1 , s3
C) s1 , s2 , s3
Page 16
D) s3 , s2 , s1
47. If the median of the following set of data is 11.5, find the value of x.
A) 11.4
B) 11.5
13.1
9.2
x
11.4
C) 11.6
D) Cannot be determined
48. The sum of all deviations equals ________.
49. Since the median is not affected by a few very small or very large observations, the
_______ is likely to be a more sensible measure of center than the ________.
50. The table below shows the attendance to the Super Bowl.
Year
1994
1995
1996
1997
1998
1999
2000
Attendance
61,545
61,062
60,190
61,382
75,482
75,206
62,784
Year
2001
2002
2003
2004
2005
2006
2007
Attendance
64,704
62,544
68,436
65,242
76,775
57,433
68,756
a) Find the 70th percentile.
b) Find the interquartile range.
Page 17
Answer Key
1. True
Section: 2
2. continuous
Section: 2
3. discrete
Section: 2
4. False
Section: 2
5. tables
Section: 2
6. B
Section: 3
7. a) 9
b) 0.563
Section: 3
8. a) 5
b) 0.3125
Section: 3
9. a) 6
b) 0.3750
Section: 3
10. A
Section: 3
11. a)
Country
Relative Frequency
Spain
0.222
England
0.204
Italy
0.204
Germany
0.111
Netherlands
0.111
Other
0.148
b) I
Section: 3
12. I
Section: 3
13. II
Section: 3
14. a)
Class Interval
Frequency
Page 18
Relative Frequency
21 - 24
25 - 28
29 - 32
33 - 36
37 - 40
41 - 44
Total
2
5
2
7
3
1
20
b) III
Section: 3
15.
16.
Section: 3
Interval
10 - 12
13 - 15
16 - 18
19 - 21
22 - 24
25 - 27
Section: 3
Frequency
2
6
6
2
3
2
17.
Section: 3
18. Mean: 9.4
Median: 11
Section: 4
19. C
Section: 4
20. Mean: 4.50
Median: 4.65
Section: 4
21. III
Section: 4
22. Q1 = 17, Q2 = 22,
Section: 4
23. B
Q3 = 23
Page 19
0.100
0.250
0.100
0.350
0.150
0.050
1.000
24.
25.
26.
27.
28.
29.
30.
Section: 4
True
Section: 4
False
Section: 4
D
Section: 4
82
Section: 4
False
Section: 5
True
Section: 5
a) 5.33, –0.67, and –4.67, respectively
b) variance: 25.3
standard deviation: 5.0
Section: 5
31. a) –3.26, –2.06, 3.54, 1.14, and 0.64, respectively
b) variance: 7.28
32.
33.
34.
35.
standard deviation: 2.70
Section: 5
s2 = 3.6
Section: 5
D
Section: 5
A
Section: 5
a) s2 = 113.7
b) s = 10.7
Section: 5
36. a) 142.80
b) 10.5
Section: 5
37. True
Section: 5
38.
a) x  34.15, s  8
b) 12/20 = 0.60,
Section: 5
20/20 = 1.00,
and
39.
Page 20
20/20 = 1.00, respectively
40.
41.
42.
43.
Minimum
6
Section: 5
None of these
Section: 6
II
Section: 6
a) I
b) 1
Section: 6
a) 65.5
Q1
15.5
Median
28.5
b) Q1 = 50, Q3 = 79
44.
45.
46.
47.
48.
49.
50.
c) 0.526
Section: 5
True
Section: 4
True
Section: 4
B
Section: 4
C
Section: 4
zero
Section: 4
mean, median
Section: 4
a) 68,436
b) 7,374
Section: 4
Page 21
Q3
41
Maximum
48