⋆ ˆ ⋆
STA1501: Descriptive Statistics and Probability
OCT/NOV Examination 2026 Preparation
Covers Past Papers: 2023 – 2024 – 2025
⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆
Statistics – Economic & Management Sciences
Exam Revision Guide
STA1501
Module Code:
Descriptive Statistics and Probability
Module Name:
OCT/NOV 2026 Prep – Covers 2023 to 2025
Paper / Exam:
University of South Africa (UNISA)
Institution:
100 (typical paper)
Total Marks:
Use this guide to revise thoroughly. Focus on understanding, not memorisation.
Exam Revision Notes | STA1501 | 2023–2025
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
Question 1 – Data Types, Frequency Distributions & Graphical Displays [20
marks]
(a) [4 marks]
Question: Distinguish between qualitative and quantitative data. Give one example of
each in the context of a business survey.
Answer:
Key Concept
Qualitative (Categorical) data describes characteristics or categories that cannot
be measured numerically. Quantitative data represents numerical measurements or
counts.
• Qualitative data: Values are labels or names that place observations into categories.
They may be nominal (no order, e.g. gender, colour, preferred mobile network) or ordinal
(ordered categories, e.g. customer satisfaction rating: poor / fair / good / excellent).
• Quantitative data: Values are numerical and arithmetic operations are meaningful.
They may be discrete (countable, e.g. number of employees) or continuous (measurable
on a scale, e.g. monthly income in rands).
Business context examples:
• Qualitative: The preferred mobile service provider of a respondent (Vodacom, MTN, Cell
C, Telkom).
• Quantitative: The monthly salary (in rands) of an employee (e.g. R18 500).
Exam Tip
In the exam, always state both the type AND a valid example. Award marks are split
equally. Ordinal vs. nominal distinction often earns an extra mark.
(b) [8 marks]
Question: The following data represents the ages (in years) of 20 employees at a com-
pany:
23, 35, 27, 41, 29, 33, 38, 25, 47, 31, 36, 28, 42, 30, 26, 39, 44, 34, 29, 37.
Page 2 of 26
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
(i) Construct a frequency distribution table using 5 classes. (ii) Draw a histogram based
on the table. (iii) Comment on the shape of the distribution.
Answer:
Step 1: Determine class width.
24
Range = max − min = 47 − 23 = 24, Class width = =5
5
Step 2: Frequency Distribution Table.
Class Interval Tally Frequency Rel. Freq.
(f ) (%)
23 – 27 |||| 4 20.0%
28 – 32 ||||| 5 25.0%
33 – 37 ||||| 5 25.0%
38 – 42 |||| 4 20.0%
43 – 47 || 2 10.0%
Total 20 100%
Step 3: Histogram (TikZ).
Age Distribution of Employees
7
6
5
Frequency
4
3
2
1
0
23 28 33 38 43
Age (years)
Step 4: Shape of distribution.
The distribution is slightly positively skewed (skewed to the right) – the majority of em-
ployees are aged 28–37, with a tail extending toward the older ages (43–47). The distribution
is roughly bell-shaped with a slight right skew.
Page 3 of 26
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
(c) [8 marks]
Question: Using the same data set from (b), calculate the (i) mean, (ii) median, (iii)
mode, and (iv) standard deviation.
Answer:
Raw data (sorted): 23, 25, 26, 27, 28, 29, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 44, 47.
(i) Mean
P
xi 23 + 25 + 26 + 27 + 28 + 29 + 29 + 30 + 31 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 41 + 42 + 44 + 4
x̄ = =
n 20
(ii) Median (n = 20, even number)
x10 + x11 33 + 34
Median = = = 33.5 years
2 2
(iii) Mode
The value 29 appears twice; all others appear once. Mode = 29 years.
(iv) Standard Deviation
x2i − nx̄2
P
2
s =
n−1
X
x2i = 232 +252 +262 +272 +282 +292 +292 +302 +312 +332 +342 +352 +362 +372 +382 +392 +412 +422 +442 +472
= 529+625+676+729+784+841+841+900+961+1089+1156+1225+1296+1369+1444+1521+1681+1764+193
23 376 − 20 × (33.65)2 23 376 − 22 650.45 725.55
s2 = = = ≈ 38.187
19 19 19
√
s≈ 38.187 ≈ 6.18 years
Page 4 of 26
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
Exam Tip
Always show the formula, substitution, and final answer. Partial marks are awarded
at each step. Use n − 1 (sample standard deviation) unless told the data is the entire
population.
Page 5 of 26
, STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
Question 2 – Measures of Position, Percentiles & Box-and-Whisker Plot [20
marks]
(a) [6 marks]
Question: The monthly salaries (in thousands of rands) of 10 employees at a firm are
listed below (already sorted in ascending order):
8, 11, 14, 17, 20, 23, 27, 32, 38, 45.
Calculate: (i) the first quartile Q1 , (ii) the third quartile Q3 , (iii) the interquartile range
(IQR), and (iv) the 60th percentile P60 .
Answer:
n = 10. The sorted data: 8, 11, 14, 17, 20, 23, 27, 32, 38, 45.
(i) First Quartile Q1 (25th percentile):
25
L25 = × 10 = 2.5 ⇒ round up to position 3 ⇒ Q1 = 14
100
(ii) Third Quartile Q3 (75th percentile):
75
L75 = × 10 = 7.5 ⇒ round up to position 8 ⇒ Q3 = 32
100
(iii) Interquartile Range:
IQR = Q3 − Q1 = 32 − 14 = 18 thousand rands
(iv) 60th Percentile P60 :
60 23 + 27
L60 = × 10 = 6 ⇒ whole number, so average positions 6 and 7 ⇒ P60 = = 25
100 2
Watch Out
p
UNISA uses the Lp = 100 × n method. If Lp is a whole number, average positions Lp
and Lp + 1. If Lp is a decimal, round up to the next whole number. Do not confuse this
with other percentile formulas.
Page 6 of 26
STA1501: Descriptive Statistics and Probability
OCT/NOV Examination 2026 Preparation
Covers Past Papers: 2023 – 2024 – 2025
⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆
Statistics – Economic & Management Sciences
Exam Revision Guide
STA1501
Module Code:
Descriptive Statistics and Probability
Module Name:
OCT/NOV 2026 Prep – Covers 2023 to 2025
Paper / Exam:
University of South Africa (UNISA)
Institution:
100 (typical paper)
Total Marks:
Use this guide to revise thoroughly. Focus on understanding, not memorisation.
Exam Revision Notes | STA1501 | 2023–2025
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
Question 1 – Data Types, Frequency Distributions & Graphical Displays [20
marks]
(a) [4 marks]
Question: Distinguish between qualitative and quantitative data. Give one example of
each in the context of a business survey.
Answer:
Key Concept
Qualitative (Categorical) data describes characteristics or categories that cannot
be measured numerically. Quantitative data represents numerical measurements or
counts.
• Qualitative data: Values are labels or names that place observations into categories.
They may be nominal (no order, e.g. gender, colour, preferred mobile network) or ordinal
(ordered categories, e.g. customer satisfaction rating: poor / fair / good / excellent).
• Quantitative data: Values are numerical and arithmetic operations are meaningful.
They may be discrete (countable, e.g. number of employees) or continuous (measurable
on a scale, e.g. monthly income in rands).
Business context examples:
• Qualitative: The preferred mobile service provider of a respondent (Vodacom, MTN, Cell
C, Telkom).
• Quantitative: The monthly salary (in rands) of an employee (e.g. R18 500).
Exam Tip
In the exam, always state both the type AND a valid example. Award marks are split
equally. Ordinal vs. nominal distinction often earns an extra mark.
(b) [8 marks]
Question: The following data represents the ages (in years) of 20 employees at a com-
pany:
23, 35, 27, 41, 29, 33, 38, 25, 47, 31, 36, 28, 42, 30, 26, 39, 44, 34, 29, 37.
Page 2 of 26
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
(i) Construct a frequency distribution table using 5 classes. (ii) Draw a histogram based
on the table. (iii) Comment on the shape of the distribution.
Answer:
Step 1: Determine class width.
24
Range = max − min = 47 − 23 = 24, Class width = =5
5
Step 2: Frequency Distribution Table.
Class Interval Tally Frequency Rel. Freq.
(f ) (%)
23 – 27 |||| 4 20.0%
28 – 32 ||||| 5 25.0%
33 – 37 ||||| 5 25.0%
38 – 42 |||| 4 20.0%
43 – 47 || 2 10.0%
Total 20 100%
Step 3: Histogram (TikZ).
Age Distribution of Employees
7
6
5
Frequency
4
3
2
1
0
23 28 33 38 43
Age (years)
Step 4: Shape of distribution.
The distribution is slightly positively skewed (skewed to the right) – the majority of em-
ployees are aged 28–37, with a tail extending toward the older ages (43–47). The distribution
is roughly bell-shaped with a slight right skew.
Page 3 of 26
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
(c) [8 marks]
Question: Using the same data set from (b), calculate the (i) mean, (ii) median, (iii)
mode, and (iv) standard deviation.
Answer:
Raw data (sorted): 23, 25, 26, 27, 28, 29, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 44, 47.
(i) Mean
P
xi 23 + 25 + 26 + 27 + 28 + 29 + 29 + 30 + 31 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 41 + 42 + 44 + 4
x̄ = =
n 20
(ii) Median (n = 20, even number)
x10 + x11 33 + 34
Median = = = 33.5 years
2 2
(iii) Mode
The value 29 appears twice; all others appear once. Mode = 29 years.
(iv) Standard Deviation
x2i − nx̄2
P
2
s =
n−1
X
x2i = 232 +252 +262 +272 +282 +292 +292 +302 +312 +332 +342 +352 +362 +372 +382 +392 +412 +422 +442 +472
= 529+625+676+729+784+841+841+900+961+1089+1156+1225+1296+1369+1444+1521+1681+1764+193
23 376 − 20 × (33.65)2 23 376 − 22 650.45 725.55
s2 = = = ≈ 38.187
19 19 19
√
s≈ 38.187 ≈ 6.18 years
Page 4 of 26
,STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
Exam Tip
Always show the formula, substitution, and final answer. Partial marks are awarded
at each step. Use n − 1 (sample standard deviation) unless told the data is the entire
population.
Page 5 of 26
, STA1501 | Exam Revision 2023–2025 Descriptive Statistics & Probability
Question 2 – Measures of Position, Percentiles & Box-and-Whisker Plot [20
marks]
(a) [6 marks]
Question: The monthly salaries (in thousands of rands) of 10 employees at a firm are
listed below (already sorted in ascending order):
8, 11, 14, 17, 20, 23, 27, 32, 38, 45.
Calculate: (i) the first quartile Q1 , (ii) the third quartile Q3 , (iii) the interquartile range
(IQR), and (iv) the 60th percentile P60 .
Answer:
n = 10. The sorted data: 8, 11, 14, 17, 20, 23, 27, 32, 38, 45.
(i) First Quartile Q1 (25th percentile):
25
L25 = × 10 = 2.5 ⇒ round up to position 3 ⇒ Q1 = 14
100
(ii) Third Quartile Q3 (75th percentile):
75
L75 = × 10 = 7.5 ⇒ round up to position 8 ⇒ Q3 = 32
100
(iii) Interquartile Range:
IQR = Q3 − Q1 = 32 − 14 = 18 thousand rands
(iv) 60th Percentile P60 :
60 23 + 27
L60 = × 10 = 6 ⇒ whole number, so average positions 6 and 7 ⇒ P60 = = 25
100 2
Watch Out
p
UNISA uses the Lp = 100 × n method. If Lp is a whole number, average positions Lp
and Lp + 1. If Lp is a decimal, round up to the next whole number. Do not confuse this
with other percentile formulas.
Page 6 of 26
