First midterm exam – 1431/1432
Question #1:
(6 marks)
1. Explain whether each of the following constitutes a population or a
sample?
a.
(P) Ages
of all students of in Computer Engineering Department at Majmaah
University.
b.
(S) Number of laptops owned by 50 families selected from Almajmaah city.
c.
(S) A group of 200 patients selected to blood test
d.
(P) Goals scored by all Football national teams participated in World Cup 2010.
2. Indicate which of the following an example of a sample with replacement
is and which is a sample without replacement.

A box contains eight balls of different colours. A ball is drawn from this box,
its colour is recorded, and it is put out the box before the next ball is drawn,
this experiment is repeated 7 times. (without replacement)

Ten students are selected from a statistics class in such a way that as soon as
a student is elected, his or her name is deleted from the list before the next
student is selected. (without replacement)
Question #2:
(5 marks)
The following are the temperatures (in degrees Fahrenheit)
observed during eight wintry days in a Midwestern city (sample):
23
14
6
-7
-2
11
16
Compute the range, variance, and standard deviation
1
21
First midterm exam – 1431/1432
Range = 23 – (-7) = 30
Variance = 113.07
Standard deviation = 10.63 degrees
Question #3:
(3 marks)
The following table gives the frequency distribution of ages for all 50
employees of a company.
Age
Number of
Employees
Class limit
18 to 30
12
18-30
31 to 43
17
18-43
44 to 56
15
18-56
57 to 69
6
18-69
Class
Boundary
18.5 to less
than 30.5
18.5 to less
than 43.5
18.5 to less
than 56.5
18.5 to less
than 69.5
Cumulative
Frequency
PRCF
12
24
29
58
44
88
50
100
Select the correct drawing of an Ogive for the cumulative percentage distribution.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 1.
2
First midterm exam – 1431/1432
Question #4:
(6 marks)
The following table gives the frequency distribution of the number of credit
cards possessed by 80 adults.
a. Find the class boundaries and class midpoints.
b. Do all classes have the same width? If so, what is this width?
(Choose the upper limit of the class previous to the first one to be -1.)
c. Prepare a cumulative frequency distribution.
d. Calculate the cumulative relative frequencies and cumulative percentages
for all classes.
Number of Credit Cards Number of Adults
0 to 3
16
4 to 7
27
8 to 11
21
12 to 15
13
16 to 19
3
Round the values of relative frequencies to 3 decimal places and the values
of percentage to 1 decimal place
a) Class boundaries and class midpoints
Class limits
Lower boundary
Upper boundary
Midpoint
Class width
0 to 3
-0.5
3.5
1.5
4
4 to 7
3.5
7.5
5.5
4
8 to 11
7.5
11.5
9.5
4
12 to 15
11.5
15.5
13.5
4
16 to 19
15.5
19.5
17.5
4
b) Yes all the classes have the same width = 3
3
First midterm exam – 1431/1432
Preparing the cumulative relative frequencies and the
cumulative
percentages for all classes
Number of
Credit Cards
0 to 3
0 to 7
0 to 11
0 to 15
0 to 19
Good Luck
4
Cumulative Cumulative relative
frequency
frequency
16
0.200
43
0.538
64
0.800
77
0.963
80
1.000
Cumulative
percentage
20.0
53.8
80.0
96.3
100.0