18 questions arranged by DBE cognitive level — data types, central tendency, grouped data, quartiles, the interquartile range, the five-number summary and box-and-whisker diagrams. Work each one on paper first, then reveal the memo.
18
practice questions
4
cognitive levels
18
worked memos
100%
independently verified
How to use this bank.
Start at Level 1 and move up — don't jump to Level 4 first.
Always sort the data first — it's the single most common lost mark on quartile questions.
For grouped data, write out the midpoints and cumulative frequencies before answering anything.
Reveal the memo only after a genuine attempt.
Accuracy note: every question below was independently solved from scratch before publication, cross-checked against its own working rather than assumed correct. These are original "Equation Station SA Practice Question" items, written to match the exact CAPS scope taught in the Summary Notes for this grade.
L1 — Knowledge 5 Qs
L2 — Routine Procedures 5 Qs
L3 — Complex Procedures 4 Qs
L4 — Problem Solving 4 Qs
28%
Level 1 | Knowledge
Direct Recall
Mean, mode, median and range of a short, ungrouped, already-manageable list.
Q1Equation Station SA Practice Question2 marks
Central Tendency
Mean of a Small Data Set
Calculate the mean of: \(3,\ 7,\ 8,\ 10,\ 12\)
Memo
✓ Add all 5 values and divide by 5: every value contributes directly to the mean.✓ \(\dfrac{3+7+8+10+12}{5}=\dfrac{40}{5}=\boxed{8}\)
✓ The mode is whichever value occurs most often — \(8\) appears three times, every other value appears once.✓ \(\boxed{\text{mode}=8}\)
Q3Equation Station SA Practice Question2 marks
Central Tendency
Median of an Odd-Sized Set
Determine the median of: \(14,\ 9,\ 22,\ 17,\ 11\)
Memo
✓ Arrange in order first — the median only makes sense once the data is sorted: \(9,11,14,17,22\)✓ With 5 values, the middle (3rd) value is the median: \(\boxed{14}\)
Q4Equation Station SA Practice Question1 mark
Dispersion
Range
Determine the range of: \(22,\ 45,\ 31,\ 8,\ 19,\ 36\)
Memo
✓ Range is the highest value minus the lowest: max \(=45\), min \(=8\).✓ \(45-8=\boxed{37}\)
Q5Equation Station SA Practice Question3 marks
Data Types
Types of Data
Classify each of the following as qualitative, quantitative discrete, or quantitative continuous data: (a) the colour of car each of 30 customers bought; (b) the number of children in each of 30 families; (c) the height (in cm) of each of 30 seedlings.
Memo
✓ (a) Colour describes a category, not a number, so it is \(\boxed{\text{qualitative}}\).✓ (b) The number of children is numerical, but only whole, countable values are possible (you can't have 2,5 children), so it is \(\boxed{\text{quantitative discrete}}\).✓ (c) Height is numerical and can take ANY value in a range (measured, not counted), so it is \(\boxed{\text{quantitative continuous}}\).
28%
Level 2 | Routine Procedures
One Established Method
An even-sized median, a modal interval, a grouped-data mean estimate, a missing value, and quartiles for an odd data set.
Q6Equation Station SA Practice Question2 marks
Central Tendency
Median of an Even-Sized Set
Determine the median of: \(12,\ 18,\ 25,\ 9,\ 30,\ 15\)
Memo
✓ Arrange in order: \(9,12,15,18,25,30\) — 6 values (even).✓ Average the two middle (3rd, 4th) values: \(\dfrac{15+18}{2}=\boxed{16{,}5}\)
Q7Equation Station SA Practice Question1 mark
Grouped Data
Identifying the Modal Interval
Four intervals have frequencies \(6,\ 14,\ 9,\ 3\) respectively. State the modal interval (by position).
Memo
✓ The modal interval is the one with the HIGHEST frequency, not the highest interval values.✓ \(14\) is the highest frequency, belonging to \(\boxed{\text{the 2nd interval}}\)
Q8Equation Station SA Practice Question3 marks
Grouped Data
Estimating the Mean of Grouped Data
Estimate the mean of the grouped data below.
Interval
Frequency
\(0\le x<10\)
5
\(10\le x<20\)
8
\(20\le x<30\)
7
Memo
✓ Midpoints: \(5,15,25\). Total frequency \(n=5+8+7=20\).✓ Estimated mean \(=\dfrac{(5)(5)+(15)(8)+(25)(7)}{20}=\dfrac{25+120+175}{20}=\dfrac{320}{20}=\boxed{16}\)
Q9Equation Station SA Practice Question3 marks
Central Tendency
Finding a Missing Value
The mean of 6 numbers is 15. Five of the numbers are \(10,\ 12,\ 18,\ 20,\ 14\). Find the sixth number.
Memo
✓ Work backward from the mean: total of all 6 numbers \(=15\times6=90\)✓ The five known numbers add up to \(10+12+18+20+14=74\)✓ Sixth number \(=90-74=\boxed{16}\)
Q10Equation Station SA Practice Question4 marks
Dispersion
Quartiles for an Odd-Sized Set
Determine \(Q_1\), the median and \(Q_3\) of: \(4,\ 9,\ 12,\ 15,\ 18,\ 21,\ 25\)
Memo
✓ Already in order, 7 values. Median (4th value) \(=15\).✓ Lower half (excluding the median): \(4,9,12\). \(Q_1\), its middle value, \(=9\).✓ Upper half: \(18,21,25\). \(Q_3\), its middle value, \(=25\).✓ \(\boxed{Q_1=9,\ \text{median}=15,\ Q_3=25}\)
22%
Level 3 | Complex Procedures
Multi-Step Methods
Quartiles for an even data set, the semi-interquartile range, a median interval from cumulative frequency, and a full five-number summary.
Q11Equation Station SA Practice Question4 marks
Dispersion
IQR for an Even-Sized Set
Determine the interquartile range of: \(11,\ 15,\ 19,\ 22,\ 26,\ 29,\ 33,\ 38\)
Memo
✓ Already in order, 8 values (even) — the whole set splits cleanly into two halves of 4.✓ Lower half: \(11,15,19,22\). \(Q_1=\dfrac{15+19}{2}=17\).✓ Upper half: \(26,29,33,38\). \(Q_3=\dfrac{29+33}{2}=31\).✓ \(\text{IQR}=Q_3-Q_1=31-17=\boxed{14}\)
Q12Equation Station SA Practice Question4 marks
Dispersion
Semi-Interquartile Range
Determine the semi-interquartile range of: \(6,\ 10,\ 13,\ 17,\ 20,\ 24,\ 28\)
Memo
✓ 7 values, already in order. Median (4th value) \(=17\), excluded from both halves.✓ Lower half: \(6,10,13\). \(Q_1=10\). Upper half: \(20,24,28\). \(Q_3=24\).✓ IQR \(=24-10=14\). Semi-IQR is HALF of this: \(\dfrac{14}{2}=\boxed{7}\)
Q13Equation Station SA Practice Question4 marks
Grouped Data
Median Interval from Cumulative Frequency
Five intervals have frequencies \(8,\ 12,\ 20,\ 15,\ 5\). State which interval (by position) contains the median.
Memo
✓ Total \(n=8+12+20+15+5=60\). Cumulative frequencies: \(8,\ 20,\ 40,\ 55,\ 60\).✓ Median position \(=\dfrac{n}{2}=30\)th value.✓ The running total passes 20 and reaches 40 in the 3rd interval: \(\boxed{\text{the 3rd interval}}\)
✓ Arrange in order: \(22,28,30,35,38,42,45,48,50\) — 9 values.✓ Minimum \(=22\), maximum \(=50\). Median (5th value) \(=38\).✓ Lower half: \(22,28,30,35\). \(Q_1=\dfrac{28+30}{2}=29\).✓ Upper half: \(42,45,48,50\). \(Q_3=\dfrac{45+48}{2}=46{,}5\).✓ \(\boxed{22,\ 29,\ 38,\ 46{,}5,\ 50}\)
22%
Level 4 | Problem Solving
Combined Skills
A percentile from a real grouped table, interpreting the IQR, comparing two data sets, and a word problem.
Q15Equation Station SA Practice Question4 marks
Grouped Data
A Percentile from a Grouped Table
For the grouped data below, identify the interval containing the lower quartile (\(Q_1\)).
Interval
Frequency
\(0\le x<10\)
5
\(10\le x<20\)
9
\(20\le x<30\)
14
\(30\le x<40\)
8
\(40\le x<50\)
4
Memo
✓ Total \(n=5+9+14+8+4=40\). Cumulative frequencies: \(5,\ 14,\ 28,\ 36,\ 40\).✓ \(Q_1\) position \(=\dfrac{n}{4}=10\)th value.✓ The running total passes 5 and reaches 14 in the 2nd interval: \(\boxed{10\le x<20}\)
Q16Equation Station SA Practice Question3 marks
Dispersion
Interpreting the IQR
A data set has \(Q_1=42\) and \(Q_3=68\). Determine the IQR, and explain in one sentence what it tells you about the middle 50% of the data.
Memo
✓ \(\text{IQR}=Q_3-Q_1=68-42=\boxed{26}\)✓ The middle 50% of the data (from \(Q_1\) to \(Q_3\)) is spread across a range of 26 units — this describes how tightly clustered the CENTRAL data is, ignoring the most extreme quarter at either end.
Q17Equation Station SA Practice Question6 marks
Central TendencyDispersion
Comparing Two Data Sets
Team A's scores: \(50,\ 55,\ 58,\ 60,\ 62,\ 65,\ 70\). Team B's scores: \(30,\ 45,\ 58,\ 60,\ 62,\ 75,\ 90\). Compare the two teams' spread of results.
Memo
✓ Team A (already sorted, 7 values): median \(=60\); lower half \(50,55,58\Rightarrow Q_1=55\); upper half \(62,65,70\Rightarrow Q_3=65\). Range \(=70-50=20\); IQR \(=65-55=10\).✓ Team B (already sorted, 7 values): median \(=60\); lower half \(30,45,58\Rightarrow Q_1=45\); upper half \(62,75,90\Rightarrow Q_3=75\). Range \(=90-30=60\); IQR \(=75-45=30\).✓ Both teams share the exact same median (60), but Team B's range and IQR are three times larger than Team A's: \(\boxed{\text{Team B's results are far more inconsistent, despite an identical median}}\)
Q18Equation Station SA Practice Question4 marks
Word Problem
A Missing Test Score
A learner's mean mark across 5 tests is 68%. Four of the marks are \(55\%,\ 72\%,\ 80\%,\ 61\%\). Determine the fifth mark.
Memo
✓ Total of all 5 marks \(=68\times5=340\)✓ The four known marks add up to \(55+72+80+61=268\)✓ Fifth mark \(=340-268=\boxed{72\%}\) (check: mean of \(55,72,80,61,72\) is \(\dfrac{340}{5}=68\)✓)