Problem Set 1
1. After the graduation ceremonies at a university, six graduates were asked
whether they were in favor of (identified by 1) or against (identified by 0)
abortion. Some information about these graduates is shown below.
Graduate
Gender
Age
Abortion
Issue
Class Rank
Maria
F
32
1
3
Robert
M
18
1
2
Tammy
F
33
0
1
Edward
M
38
0
20
Marlene
F
25
1
4
David
M
19
0
8
(a) How many elements are in the data set? Write down these elements.
(b) How many variables are in the data set? Write down these variables.
(c) How many observations are in the data set? Write down these observations.
(d) Which of the above variables are qualitative and which are quantitative?
2. Below you are given the examination scores of 20 students.
52
99
92
86
84
90
75
74
56
99
63
72
76
95
88
92
58
65
79
80
(a) Construct a frequency distribution for this data. Let the first class be 50-59
and draw a histogram.
(b) Construct a cumulative frequency distribution.
(c) Construct a relative frequency distribution.
(d) Construct a cumulative relative frequency distribution.
(e) Construct a stem-and-leaf display.
3. Below you are given the ages of a sample of 10 college students who are
enrolled in statistics.
20
18
20
Compute the following:
22
18
20
22
17
19
24
(a) The mean.
(b) The variance and the standard deviation.
(c) The coefficient of variation.
(d) The 30th percentile.
(e) The median.
(f) The mode.
(g) The interquartile range.
(h) Provide a five-number summary for the data.
(i) Show the box plot.
(j) Determine the outliers.
4. The following is a frequency distribution of grades for a statistics
examination.
Examination Grade
Frequency
40-49
3
50-59
5
60-69
11
70-79
22
80-89
15
90-99
6
Compute the following:
(a) The mean.
(b) The standard deviation.
(c) The coefficient of variation.
5. The flashlight batteries produced by one of the manufacturers are known to
have an average life of 60 hours with a standard deviation of 4 hours.
(a) At least what percentage of batteries will have a life of 54 to 66 hours?
(b) At least what percentage of the batteries will have a life of 52 to 68 hours?
(c) Determine an interval for the batteries’ lives that will be true for at least 80%
of the batteries.