10.1 ASSIGNMENT QUESTIONS: SEMESTER ONE (JULY – DECEMBER 2023)

10.1.1 BUSINESS STATISTICS 101

Question 1 [20]

The number of milkshakes sold by Milky Lane Creamery for 12 consecutive days is given
below.

89 71 85 83 92 84 67 95 104 78 102 88

2.1. Using the raw data, determine the range. (2)
2.2. Group the data into a frequency distribution with a lowest class lower limit of 60 and a
class width of 10. (5)
2.3. Determine the mean using the raw data. (3)
2.4. Draw an OGIVE curve corresponding to the data and use it to estimate the median. (10)

Question 2 [20]

The number of Golden Key candidates for at RBS of different ages in the 2023 academic
year is shown in the table below.

Candidate age (years) Number of Candidates

10 < 20 4

20 < 30 9

30 < 40 18

40 < 50 26

50 < 60 17

60 < 70 6

For these patients, determine the:

2.1 mean age of the candidates. (3)
2.2 modal age of the candidates. (3)
2.3 Median age of the candidates (4)
2.4 Determine the coefficient of variation and comment on your findings. (10)

Question 3 [20]
The Caffeine Vending Machine Company operates coffee vending machines in several office
buildings. The company wants to study the relationship that exists between the number of
cups of coffee sold per day and the number of persons working in each office. Data for this
study were collected and presented below.

LOCATION NO OF CUPS
SOLD

NO OF
PERSONS

1 10 5

2 20 6

3 30 10

4 40 13

5 50 22

3.1 Draw a scatter diagram depicting the data. (5)
3.2. Calculate the Pearson’s correlation coefficient. (9)
3.3. Determine the linear regression equation and use it to predict the number of persons
working in an office if 60 cups of coffee were sold. (6)

Question 4 [20]
4.1 A company is interested in understanding the demographics of its work force in terms of
gender and level of university education. The company conducted a survey to collect this
information and was classified as follows:

Gender Bachelor’s degree Honours degree

Male 4 6

Female 21 8

4.1.1 If a worker is selected at random from the office, what is the probability that he/she will
be in the Honours degree? (2)
4.1.2 If a worker selected is female, what is the probability that she will be in the Honours
degree? (3)
4.1.3 If a worker selected is male, what is the probability that he will be in the Honours
degree? (3)
4.1.4 If a worker selected is in the Honours degree, what is the probability of the worker
being male? (3)
4.1.5 If a worker is selected at random, what is the probability that the worker will be a male?
(2)
4.2 Suppose we have a sample space S= {7; 8; 14; 45; 63; 23; 12}; and we have events:
A= {7; 12; 23} and B= {14; 45; 63}
4.2.1 Are the two events mutually exclusive? Explain? (2)
4.2.2 Draw a Venn diagram for A ∩ B (3)
4.2.3 Calculate the probability P(A U B) (2)

Question 5

A market basket consists of three goods: apples, bananas, and oranges. The quantity and
price of each good in the base period and the current period are given below.

Quantity
(2020)

Price (2020) Quantity
(2022)

Price (2022)

Apples 20 R2 25 R2.50

Bananas 30 R1 40 R1.20

Oranges 10 R3 15 R3.50

Calculate and interpret the following price and quantity indices.
5.1 Laspeyre Price Index (5)
5.2 Paasche Price Index (5)
5.3 Laspeyre Quantity Index (5)
5.4 Paasche Price Index (5)