AMP STUDY NOTES
STA1501 · DESCRIPTIVE STATISTICS AND PROBABILITY
Complete Module
Additional Practice Problems
All eleven chapters’ additional practice problems combined into a
single volume, in order — at least ten fully worked problems per
chapter.
Chapter 1 — What is Statistics?
Chapter 2 — Graphical Descriptive Techniques
Chapter 3 — Numerical Descriptive Techniques
Chapter 4 — Data Collection and Sampling
Chapter 5 — Basic Probability
Chapter 6 — Random Variables & Discrete Distributions
Chapter 7 — Continuous Probability Distributions
Chapter 8 — Sampling Distributions
Chapter 9 — Introduction to Estimation
Chapter 10 — Introduction to Hypothesis Testing
Chapter 11 — Inference About a Population
ADDITIONAL PRACTICE PROBLEMS · ALL CHAPTERS
Independent study material. These are original practice problems, written to match the style and difficulty of
typical STA1501 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
,AMP STUDY NOTES
STA1501 · DESCRIPTIVE STATISTICS AND PROBABILITY
Chapter 1
Additional Practice Problems
Ten practice problems in the style commonly seen in STA1501
assessments, spanning data-type classification, population/sample,
and parameter/statistic identification — each with a complete,
independently worked solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These are original practice problems, written to match the style and difficulty of
typical STA1501 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
, AMP Study Notes — STA1501 — Chapter 1 Practice Problems
Chapter 1: Additional Practice Problems
Ten problems covering the full spread of Chapter 1's exam-relevant skills, each with a complete solution. Attempt
each problem before reading its solution.
Problem 1 — Classifying Three Variables
A telecom company surveys 500 customers and records: (a) the make of handset they use, (b) the number of
minutes they used last month, (c) their answer to "how would you rate our network coverage?" on the scale
poor/fair/good/excellent. Classify each variable.
Solution. (a) Handset make (Samsung, Apple, Huawei, …) is a category with no natural order — nominal.
(b) Minutes used is a real number where a difference of, say, 50 minutes always means the same thing —
interval. (c) The rating has a natural order (excellent good fair poor) but the gap between categories
isn't a consistent numerical difference — ordinal.
Problem 2 — Population, Sample, Parameter, Statistic
A national retailer has 12,000 employees. Head office wants to know the true mean number of sick days
taken per employee last year, but only has the resources to examine the records of 400 randomly chosen
employees. The mean for those 400 employees works out to 6.3 sick days. Identify the population, sample,
parameter, and statistic.
Solution. Population: all 12,000 employees. Sample: the 400 employees whose records were examined.
Parameter: the (unknown) true mean sick days across all 12,000 employees. Statistic: the computed mean
of 6.3 sick days from the 400 sampled employees.
Problem 3 — Descriptive vs Inferential
State whether each activity is descriptive or inferential statistics: (a) A store manager tallies and graphs last
week's daily sales totals. (b) An analyst uses a sample of 200 shoppers' spending habits to predict the
spending pattern of all shoppers nationwide.
Solution. (a) The manager only summarises data already collected, making no claim about anything beyond
it — descriptive. (b) The analyst uses sample data to draw a conclusion about a larger population —
inferential.
Page 2 of 5
, AMP Study Notes — STA1501 — Chapter 1 Practice Problems
Problem 4 — The Ordinal/Interval Trap: Race Finishing Position
In a 10 km race, finishers are recorded both by their finishing time (in minutes) and by their finishing
position (1st, 2nd, 3rd, …). Classify each of these two variables, and explain why they differ despite both
looking like a ranking.
Solution. Finishing time is a real number where a one-minute gap always represents the same amount of
time, regardless of whether it's the gap between 1st and 2nd place or between 50th and 51st — this is
interval data. Finishing position only tells you the order runners crossed the line in; the time gap between
1st and 2nd place could be two seconds while the gap between 50th and 51st could be five minutes, so the
position numbers themselves don't carry a consistent numerical difference — this is ordinal data. The
distinction is exactly the "consistent gap" test: time passes the test, position doesn't.
Problem 5 — Temperature and the Ratio-Folded-Into-Interval Rule
A weather station records daily maximum temperature in degrees Celsius. Some students argue this can't be
interval data because doesn't mean "no temperature at all" (so it isn't ratio data). Classify the variable
for the purposes of this module, and explain why the ratio/interval distinction doesn't change the answer.
Solution. Temperature in is a real number where a gap means the same thing anywhere on the scale
(the gap between and is the same physical difference as between and ), which
already satisfies the definition of interval data. Whether or not the variable additionally has a true zero
(making it "ratio" data in a four-level scheme) doesn't matter here, since this module folds ratio data into the
interval category for the purpose of choosing a technique. Answer: interval.
Problem 6 — Coding a Nominal Variable
A survey records employment status as one of "employed," "unemployed," "student," or "retired," coded as
respectively for data entry. A colleague claims that because the codes are numbers, the average of
the codes gives useful information about the sample. Is the colleague correct? Justify your answer using the
variable's data type.
Solution. Employment status is a category with no natural order — changing "student" from code to code
would be just as valid a coding scheme, provided every category still gets a distinct code. This makes it
nominal data. Because the numbers are arbitrary labels rather than genuine quantities, arithmetic operations
like averaging are meaningless — an "average code" of doesn't correspond to any real employment
status. The colleague is incorrect; only counts/proportions of each category are meaningful for nominal
data.
Page 3 of 5
STA1501 · DESCRIPTIVE STATISTICS AND PROBABILITY
Complete Module
Additional Practice Problems
All eleven chapters’ additional practice problems combined into a
single volume, in order — at least ten fully worked problems per
chapter.
Chapter 1 — What is Statistics?
Chapter 2 — Graphical Descriptive Techniques
Chapter 3 — Numerical Descriptive Techniques
Chapter 4 — Data Collection and Sampling
Chapter 5 — Basic Probability
Chapter 6 — Random Variables & Discrete Distributions
Chapter 7 — Continuous Probability Distributions
Chapter 8 — Sampling Distributions
Chapter 9 — Introduction to Estimation
Chapter 10 — Introduction to Hypothesis Testing
Chapter 11 — Inference About a Population
ADDITIONAL PRACTICE PROBLEMS · ALL CHAPTERS
Independent study material. These are original practice problems, written to match the style and difficulty of
typical STA1501 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
,AMP STUDY NOTES
STA1501 · DESCRIPTIVE STATISTICS AND PROBABILITY
Chapter 1
Additional Practice Problems
Ten practice problems in the style commonly seen in STA1501
assessments, spanning data-type classification, population/sample,
and parameter/statistic identification — each with a complete,
independently worked solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These are original practice problems, written to match the style and difficulty of
typical STA1501 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
, AMP Study Notes — STA1501 — Chapter 1 Practice Problems
Chapter 1: Additional Practice Problems
Ten problems covering the full spread of Chapter 1's exam-relevant skills, each with a complete solution. Attempt
each problem before reading its solution.
Problem 1 — Classifying Three Variables
A telecom company surveys 500 customers and records: (a) the make of handset they use, (b) the number of
minutes they used last month, (c) their answer to "how would you rate our network coverage?" on the scale
poor/fair/good/excellent. Classify each variable.
Solution. (a) Handset make (Samsung, Apple, Huawei, …) is a category with no natural order — nominal.
(b) Minutes used is a real number where a difference of, say, 50 minutes always means the same thing —
interval. (c) The rating has a natural order (excellent good fair poor) but the gap between categories
isn't a consistent numerical difference — ordinal.
Problem 2 — Population, Sample, Parameter, Statistic
A national retailer has 12,000 employees. Head office wants to know the true mean number of sick days
taken per employee last year, but only has the resources to examine the records of 400 randomly chosen
employees. The mean for those 400 employees works out to 6.3 sick days. Identify the population, sample,
parameter, and statistic.
Solution. Population: all 12,000 employees. Sample: the 400 employees whose records were examined.
Parameter: the (unknown) true mean sick days across all 12,000 employees. Statistic: the computed mean
of 6.3 sick days from the 400 sampled employees.
Problem 3 — Descriptive vs Inferential
State whether each activity is descriptive or inferential statistics: (a) A store manager tallies and graphs last
week's daily sales totals. (b) An analyst uses a sample of 200 shoppers' spending habits to predict the
spending pattern of all shoppers nationwide.
Solution. (a) The manager only summarises data already collected, making no claim about anything beyond
it — descriptive. (b) The analyst uses sample data to draw a conclusion about a larger population —
inferential.
Page 2 of 5
, AMP Study Notes — STA1501 — Chapter 1 Practice Problems
Problem 4 — The Ordinal/Interval Trap: Race Finishing Position
In a 10 km race, finishers are recorded both by their finishing time (in minutes) and by their finishing
position (1st, 2nd, 3rd, …). Classify each of these two variables, and explain why they differ despite both
looking like a ranking.
Solution. Finishing time is a real number where a one-minute gap always represents the same amount of
time, regardless of whether it's the gap between 1st and 2nd place or between 50th and 51st — this is
interval data. Finishing position only tells you the order runners crossed the line in; the time gap between
1st and 2nd place could be two seconds while the gap between 50th and 51st could be five minutes, so the
position numbers themselves don't carry a consistent numerical difference — this is ordinal data. The
distinction is exactly the "consistent gap" test: time passes the test, position doesn't.
Problem 5 — Temperature and the Ratio-Folded-Into-Interval Rule
A weather station records daily maximum temperature in degrees Celsius. Some students argue this can't be
interval data because doesn't mean "no temperature at all" (so it isn't ratio data). Classify the variable
for the purposes of this module, and explain why the ratio/interval distinction doesn't change the answer.
Solution. Temperature in is a real number where a gap means the same thing anywhere on the scale
(the gap between and is the same physical difference as between and ), which
already satisfies the definition of interval data. Whether or not the variable additionally has a true zero
(making it "ratio" data in a four-level scheme) doesn't matter here, since this module folds ratio data into the
interval category for the purpose of choosing a technique. Answer: interval.
Problem 6 — Coding a Nominal Variable
A survey records employment status as one of "employed," "unemployed," "student," or "retired," coded as
respectively for data entry. A colleague claims that because the codes are numbers, the average of
the codes gives useful information about the sample. Is the colleague correct? Justify your answer using the
variable's data type.
Solution. Employment status is a category with no natural order — changing "student" from code to code
would be just as valid a coding scheme, provided every category still gets a distinct code. This makes it
nominal data. Because the numbers are arbitrary labels rather than genuine quantities, arithmetic operations
like averaging are meaningless — an "average code" of doesn't correspond to any real employment
status. The colleague is incorrect; only counts/proportions of each category are meaningful for nominal
data.
Page 3 of 5
