FACULTY OF SCIENCE
DEPARTMENT OF STATISTICS
MODULE:
STAE1A1/QTPTRA2/STASCA1
CAMPUS:
DFC
ASSESSMENT:
Test 1, Semester 1, 2025
DATE:
14 March 2025
TIME:
60 minutes
MARKS:
20 = 100%
ASSESSOR(S):
Ms. M. Thanyani
INTERNAL MODERATOR:
Ms. H. Herbst
INSTRUCTIONS:
▪ This paper consists of 10 pages.
▪ This paper consists of 20 multiple-choice questions.
▪ Select only one option for each question.
▪ Answer all questions on the answer sheets provided.
▪ The use of a non-programmable calculator is allowed.
▪ Formulae are provided on page 10.
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 1
Identify which of the following statements are false.
I.
The statistics calculated from biased samples might not be good approximations of
the population parameters.
II.
Cluster sampling is not an example of probability sampling.
III.
Extreme measurements (outliers) affect the median as strongly as they do the mean.
A. Statements I and II are false.
B. Statements I and III are false.
C. Statements II and III are false.
D. Statements I, II and III are false.
Question 2
An investigation is to be carried out to assess the overall level of education of people in
Johannesburg. It has been decided that a sample will be drawn from home telephone numbers
listed in the city's phonebook, and calls will be made on a particular Friday. Which of the following
options best describes the sampling frame in this case?
A. Everyone who stays in Johannesburg and has a phone.
B. Everyone whose home phone number is listed in the city's phonebook.
C. Everyone whose home phone number is listed in the city's phonebook and is at home on
the chosen Friday.
D. The different strata of people with different educational qualifications who own a phone.
Question 3
The process of using sample statistics to make conclusions about a population is called:
A. Descriptive statistics.
B. Inferential statistics.
C. Statistical estimation.
D. Probability.
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 4
In a sample of 100 employees in a construction company, 20, or 20%, are civil engineers. Based
on the above information, the company's paper reported that "20% of all the employees at the
company are civil engineers."
Which of the following statements is/are true?
I.
The population is made up of 100 employees.
II.
The proportion reported, 20%, is a sample parameter.
III.
This report is an example of statistical inference.
IV.
The sample is the 20 students.
A. Only Statement III is true.
B. Statements I and IV are true.
C. Statements I, II and IV are true.
D. Statements I, II, III and IV are true.
Question 5
Suppose you will be given a sample of 200 data values. You are told that the minimum is 45 and
the maximum is 132. To set up a frequency distribution table and use 45 as the lower boundary
of the first class, with 13 class intervals, what is the appropriate class width?
A. 5
B. 6
C. 7
D. 8
Question 6
Two graphical techniques that are usually used to present nominal data are:
A. Bar chart and histogram.
B. Pie chart and Ogive.
C. Bar chart and pie chart.
D. Histogram and ogive.
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 7
Suppose a systematic sample of 25 items is selected from a population of 500 items. The items
in the population are numbered 1 to 500 (Item 1 to Item 500). If the 14th item (Item 14) is randomly
selected as the first item of the sample, what is the number of the 5th item selected into the
sample?
A. 20
B. 70
C. 94
D. 114
Question 8
A sample was selected from a population; which of the following statements is true?
A. The sample mean always corresponds to one of the observations in the sample.
B. Exactly half of the observations in a sample fall below the mean.
C. The sample mean will always be the most frequently occurring data value in the sample.
D. For any set of data values, the sample standard deviation can be larger than the sample
mean.
Question 9
The ages of internship candidates at a certain company are shown in the figure below.
The total number of male intern candidates in this company is:
Candidate Internship Ages
frequency
25
20
15
16
8
10
5
8
6
0
20
8
8
2
21
22
Male
8
4
2
23
24
Female
Age
A. 16
B. 22
C. 24
D. 48
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 10
An article in Transactions of the Institution of Chemical Engineers reported data from an
experiment investigating the effect of several process variables on the vapour phase oxidation of
naphthalene.
A sample of the percentage mole conversion of naphthalene to maleic anhydride is given in the
following plot. (leaf unit 0.1):
Stem
Leaf
2
0
*
8
8
3
0
1
3
*
5
5
7
8
4
0
0
0
1
*
6
8
8
5
7
7
9
Which of the following statements is correct?
A. The sample size is 10.
B. The mode is 40.
C. The distribution is symmetrically shaped.
D. The range is 37.
Question 11
With respect to Question 10, the best measures of location and spread for this data are the:
A. Mean and standard deviation.
B. Mean and interquartile range.
C. Mean and coefficient of variation.
D. Median and variance.
Question 12
With respect to Question 10, the variance for the data is:
A. 0.8464
B. 0.8858
C. 84.09
D. 88.55
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 13
The following table shows the frequency distribution of performance appraisal scores (on a scale
from 0 to 100) for 25 financial advisors:
Performance
Appraisal Score
Frequency
Relative Frequency
Cumulative
Frequency
50 - < 60
A
0.16
4
60 - < 70
8
B
12
70 - < 80
7
0.28
C
80 - < 90
4
0.16
23
90 - < 100
2
0.08
25
TOTAL:
D
Which of the following statements is correct?
I.
The values of A, B, C and D are 4, 0.32, 19 and 25.
II. According to the frequency distribution, 28% of the financial advisors achieved a performance
appraisal score in the range (70 - < 80).
III. The percentage of financial advisors who achieved a performance appraisal score of at least
80 is 24%.
A. Statements I and II are correct
B. Statements I and III are correct
C. Statements II and III are correct
D. Statements I, II and III are correct
Question 14
Chebyshev's theorem can solve these problems for a distribution with a mean of 80 and a
standard deviation of 10. At least what percentage of values will fall between 65 and 95?
A. 55.56%
B. 68.00%
C. 75.00%
D. 95.00%
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Questions 15, 16 and 17 are based on the following scenario:
A new suburb outside Johannesburg has experienced rapid growth in the last two years, mainly
because of affordable housing and the relocation of many businesses to surrounding areas. The
graph below shows the age distribution of a sample of residents between the ages of 14 and 64.
Graph of distribution of age
400
362
350
Frequency
300
240
250
200
150
100
50
79
50
31
0
[14-24)
[24-34)
[34-44)
[44-54)
[54-64)
Age (years)
Question 15
Which one of the following statements is false?
A. The estimated mean age of residents is approximately 34,79 years.
B. The estimated variance of ages is approximately 82,76.
C. The modal class is 24 ≤ x < 34.
D. Approximately 14% of residents are not older than 44 years.
Question 16
Calculate the median for this data:
A. 24.00
B. 29.00
C. 32.31
D. 33.14
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 17
Calculate the mode for this data:
A. 24.72
B. 31.19
C. 64.00
D. 362
Question 18
A comparative study was conducted on the monthly expenditure of Civil engineering and Town
and Regional planning students at UJ. The statistics selected were as follows:
CIVIL
TOWN AND
REGIONAL PLANNING
Average
Standard
deviation
N
R1350
R98
91
R1784
R101
99
Which one of the following statements is correct?
A. The variability of Civil engineering student expenditure is less than that of Town and
Regional planning students because the standard deviation is smaller.
B. Civil engineering student expenditures are relatively more variable than town and regional
planning because their coefficient of variation is higher.
C. Civil engineering students' expenditures are relatively more variable than Town and
Regional planning students' because its sample mean is smaller.
D. Both Civil and Town and Regional planning students' expenditures are equally variable.
Question 19
With reference to Question 18: If the median expenditure for Town and Regional planning
engineering students is R1810, calculate Pearson's second-order coefficient of skewness.
A. -0.77, the distribution is negatively skewed.
B. -0.80, the distribution is negatively skewed.
C. +0.77, the distribution is positively skewed.
D. +0.80, the distribution is positively skewed.
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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Question 20
A competency test has scores with a mean of 82 and a standard deviation of 2. A histogram of
the data shows that the distribution is normal. Give the two values within one standard deviation
of the mean.
A. (80 – 82)
B. (80 – 84)
C. (82 – 84)
D. (72 – 90)
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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FORMULAE
DESCRIPTIVE STATISTICS
Raw data
Central tendency
x=
Grouped data
x
x=
n
Median position =
n +1
2
 xf
n
Median position =
Median = L +
n
2
( n2 − F ) c
fm
 1 
Mode = L + 
c
 1 +  2 
Variability
( x − x )
s=
2
n −1
( x − x ) f
s=
2
n −1
CV =
s
100
x
CV =
s
100
x
Skewness
SK 2 =
3 ( x − median )
s
SK 2 =
3 ( x − median )
s
Chebysheff's
1 − 1  100


 z2 
Theorem
STAE1A1/QTPTRA2/STASCA1, Semester Test 1, March 2025
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