Midterm 1:
90. 11. 14
1.
(15%)
Five observations taken for two variables follows:
X
Y
6
6
11
9
15
6
21
17
27
12
(a) Develop a scatter diagram for these data. What does the scatter diagram indicate about a relationship between X and Y ?
(b) Compute and interpret the sample covariance.
(c) Compute and interpret the sample correlation coefficient.
2.
(20%)
A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.
Male
Female
Total
Management
40
30
70
Marketing
0
30
30
Others
30
70
100
Total
70
130
200
(a) What is the probability of selecting an individual who is majoring in
Marketing?
(b) Given that a person is female, what is the probability of selecting an individual who is majoring in Management?
(c) Given that a person is male, what is the probability that he is majoring in Management?
(d) Let A denote the event that a student is male, let B denote the event that a student is majoring in Management, and let C denote the event that a student is majoring in Marketing. Are events A and B independent? Are events A and C mutually exclusive?
3.
(10%)
The following frequency distribution shows the time (in minutes) that a sample of students use the computer terminals per day.
Time
Frequency
20-39
2
40-59
4
60-79
6
80-99 100-119
4 2
1

(a) Compute the mean
(b) Compute the coefficient of variation.
4.(25%)
The data for the number of units produced by a production employee during the most recent 20 days are shown here.
160 170 181 156 176 148 200 179 162 150
162 156 179 178 151 157 154 179 152 156
Suppose the number of class is 5.
(a) Construct a frequency distribution and relative frequency distribution.
(b) Construct a cumulative frequency distribution and cumulative percent distribution.
(c) Construct a histogram.
(d) Construct a ogive.
(e) Construct a stem-and-leaf display.
5. (35%)
(a) Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and
25. Compute
(i) 20 th , 25 th , 65 th , and 75 th percentile.
(ii) Compute the mode.
(iii) Compute the standard deviation.
(iv) Compute the z-scores for every data.
(v) Construct the Box plot.
(b) Show that i n 

1
 x i
 x
 z i
 z

 i n 

1 x i z i
 n x z
, where x n 
 i

1 n x i
and z n 
 i

1 n z i
.
(c) 10 students’ birthdays are in this month (total 30 days). What is the probability of two students’ birthdays (among 10 students) being today?
2