UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Economic and Management Sciences
⋄
ASSIGNMENT 01
Statistics for Beginners – STA1505 – Year Module 2026
⋄
Module Code: STA1505
Module Name: Statistics for Beginners
Assignment No.: 01
Unique Number: 346278
Due Date: 21 May 2026
Year: 2026
Submitted in partial fulfilment of the requirements for STA1505
at the University of South Africa.
,UNISA | STA1505 Assignment 01 – 2026
Question 1: Statistical Terms, Variables, and Measurement Scales [17 marks]
1.1 Matching Statistical Terms to Descriptions [5 marks]
Question: A research team conducted a study at a regional weather station to analyse the
average annual rainfall (in mm) recorded across various towns in a province over the past
decade. Match each of the statistical terms (1–5) with the correct corresponding description
(a–e).
Terms:
1. Population
2. Statistic
3. Parameter
4. Sample
5. Variable data
Descriptions:
a. The annual rainfall recorded for one specific town in the province over the past decade.
b. 412 mm, 389 mm, 520 mm, 467 mm, 398 mm.
c. A randomly selected group of 20 towns from the province used in the study.
d. All towns in the province for which annual rainfall was recorded over the past decade.
e. The average annual rainfall across all towns in the province over the past decade.
Answer:
Table 1: Matched Statistical Terms and Descriptions
No. Term Match Description
1. Population d All towns in the province for which annual rainfall
was recorded over the past decade.
2. Statistic b 412 mm, 389 mm, 520 mm, 467 mm, 398 mm.
3. Parameter e The average annual rainfall across all towns in the
province over the past decade.
4. Sample c A randomly selected group of 20 towns from the
province used in the study.
5. Variable data a The annual rainfall recorded for one specific town in
the province over the past decade.
Page 1 of 10
,UNISA | STA1505 Assignment 01 – 2026
Key Distinction
Population vs. Sample: The population is every unit being studied (all towns in the
province). A sample is a smaller group pulled from that population to represent it. A
statistic is calculated from the sample; a parameter describes the whole population.
Page 2 of 10
,UNISA | STA1505 Assignment 01 – 2026
1.2 Type and Measurement Scale of Variables [12 marks]
Question: State whether each of the following variables is qualitative or quantitative, and
indicate its measurement scale.
Answer:
Table 2: Variable Classification and Measurement Scale
No. Variable Type Measurement Scale
◦
a) Temperature (in C) at a weather Quantitative Interval. Temperature has no
station each day. (continuous) true zero; 0◦ C does not mean “no
temperature.” Differences between
values are meaningful, but ratios
are not.
b) Weather conditions classified as Qualitative (cat- Nominal. These are categories
sunny, cloudy, rainy, or stormy. egorical) with no natural order between
them.
c) Ranking of cities from most pol- Qualitative (or- Ordinal. There is a clear order
luted to least polluted. dinal) (most to least polluted), but the
gaps between ranks are not equal
or measurable.
d) Jersey numbers worn by athletes in Qualitative (cat- Nominal. Numbers here are labels
a marathon race. egorical) only. They identify athletes but
do not represent any measured
quantity.
e) Number of rainy days recorded in a Quantitative Ratio. Counts of days have a true
city over a calendar year. (discrete) zero (no rainy days is genuinely
zero), and ratios between values
carry meaning.
f) Names of provinces in South Qualitative (cat- Nominal. Province names are
Africa. egorical) identifiers with no order and no
numeric value.
Key Distinction
Interval vs. Ratio: Both scales have equal, measurable gaps between values. The
difference is that ratio scales have a true, meaningful zero point – where zero actually
means “none.” Temperature in ◦ C has an arbitrary zero, so it is interval. A count of
rainy days starts at zero meaning “no rainy days,” making it ratio.
Critical Consideration
Jersey numbers (d) are a common trap. Students often classify them as quantitative
because they look like numbers. They are not – the numbers do not represent quantity;
you cannot say that jersey 20 is “twice” jersey 10 in any meaningful sense.
Page 3 of 10
, UNISA | STA1505 Assignment 01 – 2026
Question 2: Sampling Methods [10 marks]
Question: A study estimates the average number of hours per week that employees at a large
retail chain spend on job-related training. Determine the appropriate type of sampling method
used in each of the following cases.
2.1 Sampling by Job Category [2 marks]
Question: A sample of 120 employees is taken by first grouping all employees by job category
(Cashiers, Supervisors, Stock Controllers, and Managers), then selecting 30 employees from
each job category.
Answer:
This is Stratified random sampling.
The full workforce is divided into non-overlapping subgroups (strata) based on a shared char-
acteristic – in this case, job category. A fixed number of participants (30) is then randomly
selected from each stratum. This method ensures every job category appears in the sample,
which gives a more representative picture of training hours across the whole retail chain.
Implementation Insight
Stratified sampling is particularly useful when the population has meaningful subgroups
that may behave differently. Here, managers are likely to spend different hours on train-
ing compared to cashiers, so keeping them in separate strata before sampling prevents
any group from being missed or over-represented.
2.2 Every 40th Employee Selected [2 marks]
Question: A random number generator selects one employee from an alphabetical list. Start-
ing with that person, every 40th employee is selected until 80 employees have been chosen.
Answer:
This is Systematic random sampling.
A random starting point is chosen, and then every k-th unit is selected from the list at regular
intervals. Here, k = 40. Systematic sampling is straightforward to carry out in practice and
Page 4 of 10
College of Economic and Management Sciences
⋄
ASSIGNMENT 01
Statistics for Beginners – STA1505 – Year Module 2026
⋄
Module Code: STA1505
Module Name: Statistics for Beginners
Assignment No.: 01
Unique Number: 346278
Due Date: 21 May 2026
Year: 2026
Submitted in partial fulfilment of the requirements for STA1505
at the University of South Africa.
,UNISA | STA1505 Assignment 01 – 2026
Question 1: Statistical Terms, Variables, and Measurement Scales [17 marks]
1.1 Matching Statistical Terms to Descriptions [5 marks]
Question: A research team conducted a study at a regional weather station to analyse the
average annual rainfall (in mm) recorded across various towns in a province over the past
decade. Match each of the statistical terms (1–5) with the correct corresponding description
(a–e).
Terms:
1. Population
2. Statistic
3. Parameter
4. Sample
5. Variable data
Descriptions:
a. The annual rainfall recorded for one specific town in the province over the past decade.
b. 412 mm, 389 mm, 520 mm, 467 mm, 398 mm.
c. A randomly selected group of 20 towns from the province used in the study.
d. All towns in the province for which annual rainfall was recorded over the past decade.
e. The average annual rainfall across all towns in the province over the past decade.
Answer:
Table 1: Matched Statistical Terms and Descriptions
No. Term Match Description
1. Population d All towns in the province for which annual rainfall
was recorded over the past decade.
2. Statistic b 412 mm, 389 mm, 520 mm, 467 mm, 398 mm.
3. Parameter e The average annual rainfall across all towns in the
province over the past decade.
4. Sample c A randomly selected group of 20 towns from the
province used in the study.
5. Variable data a The annual rainfall recorded for one specific town in
the province over the past decade.
Page 1 of 10
,UNISA | STA1505 Assignment 01 – 2026
Key Distinction
Population vs. Sample: The population is every unit being studied (all towns in the
province). A sample is a smaller group pulled from that population to represent it. A
statistic is calculated from the sample; a parameter describes the whole population.
Page 2 of 10
,UNISA | STA1505 Assignment 01 – 2026
1.2 Type and Measurement Scale of Variables [12 marks]
Question: State whether each of the following variables is qualitative or quantitative, and
indicate its measurement scale.
Answer:
Table 2: Variable Classification and Measurement Scale
No. Variable Type Measurement Scale
◦
a) Temperature (in C) at a weather Quantitative Interval. Temperature has no
station each day. (continuous) true zero; 0◦ C does not mean “no
temperature.” Differences between
values are meaningful, but ratios
are not.
b) Weather conditions classified as Qualitative (cat- Nominal. These are categories
sunny, cloudy, rainy, or stormy. egorical) with no natural order between
them.
c) Ranking of cities from most pol- Qualitative (or- Ordinal. There is a clear order
luted to least polluted. dinal) (most to least polluted), but the
gaps between ranks are not equal
or measurable.
d) Jersey numbers worn by athletes in Qualitative (cat- Nominal. Numbers here are labels
a marathon race. egorical) only. They identify athletes but
do not represent any measured
quantity.
e) Number of rainy days recorded in a Quantitative Ratio. Counts of days have a true
city over a calendar year. (discrete) zero (no rainy days is genuinely
zero), and ratios between values
carry meaning.
f) Names of provinces in South Qualitative (cat- Nominal. Province names are
Africa. egorical) identifiers with no order and no
numeric value.
Key Distinction
Interval vs. Ratio: Both scales have equal, measurable gaps between values. The
difference is that ratio scales have a true, meaningful zero point – where zero actually
means “none.” Temperature in ◦ C has an arbitrary zero, so it is interval. A count of
rainy days starts at zero meaning “no rainy days,” making it ratio.
Critical Consideration
Jersey numbers (d) are a common trap. Students often classify them as quantitative
because they look like numbers. They are not – the numbers do not represent quantity;
you cannot say that jersey 20 is “twice” jersey 10 in any meaningful sense.
Page 3 of 10
, UNISA | STA1505 Assignment 01 – 2026
Question 2: Sampling Methods [10 marks]
Question: A study estimates the average number of hours per week that employees at a large
retail chain spend on job-related training. Determine the appropriate type of sampling method
used in each of the following cases.
2.1 Sampling by Job Category [2 marks]
Question: A sample of 120 employees is taken by first grouping all employees by job category
(Cashiers, Supervisors, Stock Controllers, and Managers), then selecting 30 employees from
each job category.
Answer:
This is Stratified random sampling.
The full workforce is divided into non-overlapping subgroups (strata) based on a shared char-
acteristic – in this case, job category. A fixed number of participants (30) is then randomly
selected from each stratum. This method ensures every job category appears in the sample,
which gives a more representative picture of training hours across the whole retail chain.
Implementation Insight
Stratified sampling is particularly useful when the population has meaningful subgroups
that may behave differently. Here, managers are likely to spend different hours on train-
ing compared to cashiers, so keeping them in separate strata before sampling prevents
any group from being missed or over-represented.
2.2 Every 40th Employee Selected [2 marks]
Question: A random number generator selects one employee from an alphabetical list. Start-
ing with that person, every 40th employee is selected until 80 employees have been chosen.
Answer:
This is Systematic random sampling.
A random starting point is chosen, and then every k-th unit is selected from the list at regular
intervals. Here, k = 40. Systematic sampling is straightforward to carry out in practice and
Page 4 of 10
