MAIN ASSESSMENT

SUBJECT: QUANTITATIVE TECHNIQUES SUBJECT CODE: KWN10AB / QTH115E

PROGRAMME: PROGRAMME CODE:

N DIP: MANAGEMENT BBNDBU
N DIP: COST AND MANAGEMENT ACCOUNTING BRNDCO
N DIP: MUNICIPAL ADMINISTRATION BRHSAB

ASSESSOR: DR DH DELPORT MODERATOR:

DATE: 31 AUGUST 2020 SESSION: 09H00

DURATION: 8 HOURS TOTAL: 100

STATIONERY:
1. MULTIPLE CHOICE ANSWER SHEET
2. CALCULATOR

INSTRUCTIONS TO CANDIDATES

1. MAKE SURE THAT YOUR QUESTION PAPER CONSISTS OF 13 PAGES.

2. ANSWER ALL THE QUESTIONS.

3. MAKE USE OF TWO DECIMAL PLACES IN ALL YOUR CALCULATIONS, UNLESS INSTRUCTED
OTHERWISE.

4. ANSWERS MUST BE PROVIDED ON THE MULTIPLE CHOICE ANSWER SHEET

 KWN10AB: MAIN2 ASSESSMENT

1. …………….. is defined as a set of mathematically based tools and techniques to transform

raw data into a few summary measures that represent useful and usable information to
support effective decision making.

(A) Information
(B) Data
(C) Statistics
(D) Management decision making
(E) None of the above

2. The transformation process from data to information looks as follow:

(A) Data ̶ Statistical analysis ̶ Information ̶ Management decision making

(B) Statistical analysis ̶ Data ̶ Management decision making ̶ Information
(C) Information ̶ Management decision making ̶ Data ̶ Statistical analysis
(D) Management decision making ̶ Data ̶ Statistical analysis ̶ Information
(E) None of the above

3. Statistical modelling:

(A) condenses sample data into a few summary descriptive measures

(B) generalizes sample findings to the broader population
(C) builds models of relationships between random variables
(D) test for genuine patterns or relationships in the population based on sample data
(E) None of the above

4. Is the following example qualitative or quantitative:

A consumer’s choice of mobile phone service provider is either Vodacom, MTN, Cell C or
Telkom

(A) Quantitative
(B) Qualitative
(C) None of the above

ASSESSOR MODERATOR
 KWN10AB: MAIN3 ASSESSMENT

5. The sample statistic for the statistical measure “Mean” is:

(A) µ
(B) 𝑥̅
(C) σ
(D) π
(E) None of the above

6. The sample statistic for the statistical measure “Variance” is:

(A) s
(B) 𝑥̅
(C) σ
(D) 𝑠2
(E) None of the above

7. The population parameter for the statistical measure “Variance” is:

(A) σ
(B) 𝜎2
(C) V
(D) 𝑠2
(E) None of the above

8. The population parameter for the statistical measure “Mean” is:

(A) µ
(B) 𝑥̅
(C) σ
(D) π
(E) None of the above

9. A population parameter:

(A) is a subset of a population

(B) is categorical data, but has an implied ranking between the different categories of
the qualitative random variable
(C) is the actual values (numbers) or outcomes recorded on a random variable
(D) is a measure that describes a characteristic of a population
(E) None of the above

ASSESSOR MODERATOR
 KWN10AB: MAIN4 ASSESSMENT

Question 10 – 13 is based on the following:

The number of students enrolled in the first year of a business course at a technical college is
shown in the following table for each of 7 years:

Year Enrolment F(<)

2003 160 A
2004 192 B
2005 221 C
2006 301 D
2007 280 E
2008 298 F
2009 316 G

10. What is the percentage of students who enrolled in 2008?

(A) 1768
(B) 16.86
(C) 298
(D) 0.1686
(E) None of the above

11. What is the percentage of students who enrolled in 2004?

(A) 192
(B) 352
(C) 0.11
(D) 10.86
(E) None of the above

12. The value of C in the table is:

(A) 221
(B) 2005
(C) 573
(D) 12.5
(E) None of the above

ASSESSOR MODERATOR
 KWN10AB: MAIN5 ASSESSMENT

13. The value of F in the table is:

(A) 16.86%
(B) 298
(C) 2008
(D) 1452
(E) None of the above

Question 14 – 22 is based on the following:

The sales of vacuum cleaners in a department store for the first 10 weeks of the year are:

87 54 65 43 78 32 76 66 54 75

14. The sample size is:

(A) 10
(B) 63
(C) 630
(D) 87
(E) None of the above

15. The arithmetic mean is:

(A) 10
(B) 630
(C) 87
(D) 63
(E) None of the above

16. The range is:

(A) 54
(B) 55
(C) 63
(D) 10
ASSESSOR MODERATOR
 KWN10AB: MAIN6 ASSESSMENT

(E) None of the above

17. The third quartile is:

(A) 78
(B) 76.5
(C) 76
(D) 8.25
(E) None of the above

18. The median is:

(A) 63
(B) 10
(C) 54
(D) 65.5
(E) None of the above

19. The variance is:

(A) 17.16
(B) 19.26
(C) 42340
(D) 294.4
(E) None of the above

20. The standard deviation is:

(A) 17.16
(B) 19.26
(C) 42340
(D) 294.4
(E) None of the above

21. The mode is:

(A) 54
(B) 63
(C) 65.5
(D) 78
(E) None of the above

ASSESSOR MODERATOR
 KWN10AB: MAIN7 ASSESSMENT

22. The first quartile position is?

(A) 2.25
(B) 51.25
(C) 43
(D) 2.75
(E) None of the above

Question 23 – 27 is based on the following:

The following table shows the promotion status of police officers over the past two years.

Men Women
Promoted 288 36
Not promoted 672 204

23. P(Not promoted):

(A) 204/876
(B) 672/876
(C) 204/1200
(D) 876/1200
(E) None of the above

24. P(Women and is promoted):

(A) 36/240
(B) 36/1200
(C) 240/1200
(D) 240
(E) None of the above

25. P(Men or is not promoted):

(A) 672/960
(B) 1164/1200

ASSESSOR MODERATOR
 KWN10AB: MAIN8 ASSESSMENT

(C) 672
(D) 672/1200
(E) None of the above

26. P(Men):

(A) 288/960
(B) 672/960
(C) 960/1200
(D) 960
(E) None of the above

27. P(Promoted given women):

(A) 36/240
(B) 36/1200
(C) 36/324
(D) 240/1200
(E) None of the above

Question 28 – 30 is based on the following:

A college that specialises in training people for top-level management positions administers various
types of physical and psychological tests. In one such test, objects must be assembled and pictures
arranged in order. Although the maximum possible score for this test is 130, the college has found
that results in the past have followed an approximate normal distribution with a mean of 91.7 and
a standard deviation of 8.3. What percentage of people obtain scores in the following ranges?
[Round off the z scores to 2 decimal places and use all digits as they are in the table]

28. Less than 105?

(A) 1.60
(B) 0.4452
(C) 0.0548
(D) 0.9452
(E) None of the above

29. Above 74?

ASSESSOR MODERATOR
 KWN10AB: MAIN9 ASSESSMENT

(A) -2.13
(B) 0.9834
(C) 0.4834
(D) 0.0166
(E) None of the above

30. Between 80 and 100?

(A) -1.41
(B) 0.7620
(C) 0.0794
(D) 0.41
(E) None of the above

ASSESSOR MODERATOR
 KWN10AB: MAIN10 ASSESSMENT

FORMULAE

𝑛
𝑐 ( 2 − 𝑓(<))
𝑀𝑒 = + 𝑂𝑚𝑒
𝑓

𝑐(𝑓𝑚 − 𝑓𝑚−1 )
𝑀𝑜 = 𝑂𝑚𝑜 +
2𝑓𝑚 − 𝑓𝑚−1 − 𝑓𝑚+1

𝑛
𝑐 ( 4 − 𝑓(<))
𝑄1 = 𝑂𝑞1 +
𝑓𝑞1

3𝑛
𝑐 ( 4 − 𝑓(<))
𝑄3 = 𝑂𝑞3 +
𝑓𝑞3

∑ 𝑥𝑖
𝑥̃ =
𝑛

∑ 𝑓𝑖 𝑥𝑖
𝑥̃ =
∑ 𝑓𝑖

𝑛+1
𝑄1 use
4

ASSESSOR MODERATOR
 KWN10AB: MAIN11 ASSESSMENT

3 × (𝑛 + 1)
𝑄3 use
4

∑ 𝑓𝑚
𝑥̃ ∶=
∑𝑓

Range = 𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛 + 1

∑ 𝑥𝑖2 − 𝑛𝑥̅ 2
𝑠2 =
(𝑛 − 1)

∑(𝑥𝑖 − 𝑥̅ )2
𝑠2 =
(𝑛 − 1)

𝑠 = √𝑠 2

𝑠
𝐶𝑉 = %
𝑥̅

3(mean – median)
𝑆𝐾𝑝 =
standard deviation

P(A or B) = P(A) + P(B)

ASSESSOR MODERATOR
 KWN10AB: MAIN12 ASSESSMENT

P(A or B) = P(A) + P(B) - P(A and B)

P(A and B) = P(A) × P(B)

P(A) + P(B) = 1

P(A and B)
P(A ∕ B) =
P(B)

P (not A ) = 1 − P(A)

P ( A or B ) = P(A) + P(B) − P(A andB)

P (not[A or B]) = P([not A]and[not B])

P (not[A andB]) = P([not A]or [not B])

P(at least n successful outcomes) = 1 – P(less than n successful outcomes)

𝒙− 𝝁
𝒛=
𝝈

𝒙 = 𝝁 + 𝒛𝝈

̅− 𝝁
𝒙
𝒛= 𝝈
⁄ 𝒏
√

ASSESSOR MODERATOR