8 exam-style question sets on Data handling (Paper 1), each with a hint and a fully worked answer. The app holds 40 questions on this section in total, including variants of every set below, and lets you mark yourself part by part.
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Question 1
A taxi association counted the passengers who boarded at two of its ranks, Rank A and Rank B, during the morning peak on a Monday. The graph below shows the number of passengers per half-hour time slot.
- aHow many passengers boarded at Rank B between 06:00 and 06:30? (2)
- bIn which time slot did exactly 36 passengers board at Rank A? (2)
- cWhich ONE of the statements below is the best description of how the number of passengers at Rank B changed during the morning? - A Passenger numbers climbed until the busiest time slot and fell away after that. - B Passenger numbers fell, recovered, and then fell again in the last time slot. - C Passenger numbers were low at first and rose in every time slot. (2)
- dA passenger is picked at random from everybody who boarded between 06:30 and 07:00. The probability that this passenger boarded at Rank A is 0,75. Write 0,75 as a common fraction in its simplest form. (2)
- eHow many passengers boarded at the two ranks altogether between 07:00 and 07:30? (3)
This question has a diagram, shown in the app.
Hint
Read each bar against the gridlines (the faint lines are 2 passengers apart), and check the key so that you use the correct rank.
Worked answer
a) 6 passengers ✓✓RG
b) 06:30–07:00 ✓✓RG
c) B ✓✓A — Rank B goes 16 → 12 → 6 (down), then 12 → 26 (up), then 18 (down).
d) 0,75 = ✓M = ✓S
e) Rank A: 24 ✓RG Rank B: 26 ✓RG
Total = 24 + 26 = 50 passengers ✓CA
Modelled on Nov 2024 Paper 1, Question 1.1 — same skills, new scenario.
Question 2
Kwela Pharmacies and Umoya Health are two pharmacy chains. GRAPH 1 shows the total number of branches of each chain from 2015 to 2024, and GRAPH 2 shows the total number of employees of each chain over the same period. The values for 2024 are printed on the graphs.
- aIn which year did the number of employees of Umoya Health drop for the first time? (2)
- bKwela Pharmacies expects to have 38,5% more branches in 2030 than it had in 2024. Calculate the number of branches that the chain expects to have in 2030. (3)
- cA shareholder claims that, in 2024, Kwela Pharmacies had more employees for every branch than Umoya Health had. Verify, showing ALL calculations, whether this claim is valid. (6)
- dOne of the years on GRAPH 1 is chosen at random. Determine, as a percentage, the probability that Kwela Pharmacies had fewer than 550 branches in that year. (3)
Hint
'Employees per branch' is a rate: divide the number of employees by the number of branches for EACH chain, using the 2024 values.
Worked answer
a) 2020 ✓✓RG (5 200 in 2019 dropped to 5 000 in 2020)
b) Expected number = 760 + 38,5% of 760 ✓M
= 760 × 1,385 = 1 052,6 ✓A
≈ 1 053 branches ✓R
c) Kwela: 9 880 ÷ 760 ✓RG ✓M = 13 employees per branch ✓A
Umoya: 6 440 ÷ 460 ✓M = 14 employees per branch ✓A
Umoya Health had MORE employees per branch (14 > 13), so the claim is NOT valid ✓J
d) Years with fewer than 550 branches: 2015, 2016, 2017, 2018, 2020 → 5 years ✓RG
P = × 100% ✓M = 50% ✓A
Modelled on Nov 2024 Paper 1, Question 3.1 — same skills, new scenario.
Question 3
A clinic manager studied how long patients waited before they were helped. On a particular Monday 412 patients visited the clinic, and the waiting times (in minutes) of a selected number of these patients were recorded.
WAITING TIMES (IN MINUTES) OF THE SELECTED PATIENTS
| 25 | 15 | 19 | 18 | 28 | 18 | 45 | 14 |
| 27 | 4 | 16 | 15 | 6 | 7 | 10 | 36 |
| 9 | 26 | 21 | 30 | 12 | 12 | 24 | 22 |
| 34 | 148 | 32 | 22 | 40 | 20 |
The values are repeated below from the smallest to the largest. The box-and-whisker plot of the data is given too, but it has not been completed.
| 4 | 6 | 7 | 9 | 10 | 12 | 12 | 14 |
| 15 | 15 | 16 | 18 | 18 | 19 | 20 | 21 |
| 22 | 22 | 24 | 25 | 26 | 27 | 28 | 30 |
| 32 | 34 | 36 | 40 | 45 | 148 |
- aHow many patients are in the SAMPLE of this study, and how many are in the POPULATION? (3)
- bDuring which stage of the data-handling cycle (A–E) are measures of central tendency and of spread worked out? - A Collecting data - B Classifying and organising data - C Summarising data - D Representing data - E Analysing and interpreting data (2)
- cExplain why 148 is called an outlier in this data set. (2)
- dDetermine the upper quartile (Q3) of the ranked data. (3)
- eNomsa says: 'Leave out the outlier, and the interquartile range (IQR) of the values that remain is 14,5.' Verify, showing ALL calculations, whether Nomsa is correct. (5)
This question has a diagram, shown in the app.
Hint
When a value is removed the number of values changes, so the positions of Q1 and Q3 must be found again.
Worked answer
a) Sample size = 30 patients ✓✓RT
Population size = 412 patients ✓RT
b) C ✓✓A — the mean, median, mode, range and quartiles SUMMARISE a data set.
c) 148 is much larger than all the other values ✓✓O (the next value is 45; it lies far away from the rest of the data).
d) There are 30 values, so the upper half is the last 15 values: 21, 22, 22, 24, 25, 26, 27, 28, 30, 32, 34, 36, 40, 45, 148 ✓M
Q3 is the middle of the upper half (8th value) ✓M
Q3 = 28 ✓A
e) Without 148 there are 29 values.
Lower half = first 14 values → Q1 = 13 (7th and 8th values) ✓M ✓A
Upper half = last 14 values → Q3 = 27,5 ✓A
New IQR = 27,5 − 13 = 14,5 ✓CA
The statement is VALID ✓J
Modelled on Nov 2024 Paper 1, Question 3.2 — same skills, new scenario.
Question 4
A large high school writes its examinations in one of three venues. The maximum number of candidates that each venue can seat is:
- School hall: 500 candidates
- Gymnasium: 300 candidates
- Media centre: 120 candidates
TABLE 1: NUMBER OF CANDIDATES PER EXAMINATION SESSION
| EXAMINATION | ||||||||
|---|---|---|---|---|---|---|---|---|
| November | 140 | 420 | 310 | 95 | 260 | 480 | 180 | 350 |
| June | 390 | 110 | 275 | 60 | 450 | 230 |
- aEvery session is written in the SMALLEST venue that can seat all its candidates. A session is chosen at random from all the June and November sessions. Write, as a decimal rounded to TWO decimal places, the probability that it had to be written in the school hall. (3)
- bDetermine the median number of candidates per session for the November examination. (3)
- cThe chief invigilator says that the number of candidates per session had exactly the same range in June as in November. Verify, showing ALL calculations, whether his statement is valid. (5)
Hint
The school hall is only needed when a session has MORE than 300 candidates — count those sessions in BOTH rows.
Worked answer
a) Number of values that need the school hall: 420, 310, 480, 350, 390, 450 → 6 ✓RT
Total number of values = 8 + 6 = 14 ✓RT
P = = 0,43 ✓CA
b) In order: 95; 140; 180; 260; 310; 350; 420; 480 ✓M
Median = (260 + 310) ÷ 2 ✓M = 285 ✓A
c) Range November = 480 − 95 ✓M = 385 ✓A
Range June = 450 − 60 ✓M = 390 ✓A
385 ≠ 390, so the statement is NOT valid ✓J
Modelled on Nov 2024 Paper 1, Question 4.2 — same skills, new scenario.
Question 5
An education district collected information on the number of learners in its high schools at the start of 2025. The results are summarised in the table below. The number of girls in Grade 10 was seven thousand two hundred and fourteen.
NUMBER OF LEARNERS IN THE DISTRICT PER GRADE
| GRADE | BOYS | GIRLS | TOTAL | % OF ALL LEARNERS |
|---|---|---|---|---|
| Grade 8 | 6 412 | 6 538 | 12 950 | 21,6 |
| Grade 9 | 6 105 | 6 290 | 12 395 | 20,7 |
| Grade 10 | 6 890 | A | 14 104 | 23,5 |
| Grade 11 | 5 236 | 5 874 | 11 110 | 18,5 |
| Grade 12 | 4 318 | 5 023 | 9 341 | B |
| TOTAL | 28 961 | 30 939 | 59 900 | 100,0 |
- aIdentify the grade with the lowest number of boys. (2)
- bState whether the number of learners in a grade is discrete or continuous data. (2)
- cName the instrument that the district most probably sent to the schools to collect this data. (2)
- dWrite down the total number of learners in the high schools of this district. (2)
- eWrite down, in numerals, the missing value A. (2)
- fCalculate the missing value B, the number of Grade 12 learners as a percentage of all the learners. Round your answer to ONE decimal place. (3)
Hint
The value A is written out in words in the text above the table.
Worked answer
a) Grade 12 ✓✓RT (4 318 is the smallest value in that column)
b) Discrete ✓✓A (learners are counted; you cannot have a part of a learner)
c) A questionnaire / survey form ✓✓A
d) 59 900 ✓✓RT (bottom row of the TOTAL column)
e) A = 7 214 ✓✓A (seven thousand two hundred and fourteen)
f) B = × 100% ✓RT ✓M
= 15,6% ✓A
Modelled on Nov 2025 Paper 1, Question 1.3 — same skills, new scenario.
Question 6
The sports office of a university analysed the membership of its six biggest sports clubs for 2025. The percentage and the number of male and female members per club are shown in the table below. One value was left out.
MEMBERSHIP OF SIX SPORTS CLUBS
| CLUB | MALE (%) | MALE MEMBERS | FEMALE (%) | FEMALE MEMBERS |
|---|---|---|---|---|
| Athletics | 55% | 352 | 45% | 288 |
| Netball | 4% | 18 | 96% | 432 |
| Hockey | 42% | 210 | 58% | ? |
| Rugby | 85% | 323 | 15% | 57 |
| Swimming | 48% | 120 | 52% | 130 |
| Tennis | 46% | 138 | 54% | 162 |
- aDetermine the median of the percentages of MALE members of the six clubs. (4)
- bOne of the six clubs is chosen at random. Determine, as a decimal rounded to THREE decimal places, the probability that the club has fewer male members than female members. (3)
- cUse the male members of the hockey club to calculate the total number of members of the hockey club. (2)
- dThe chairperson of the hockey club states that the club has 100 more female members than male members. Verify, showing ALL calculations, whether this statement is valid. (4)
Hint
For the median of six values, arrange them in order and find the mean of the 3rd and 4th values.
Worked answer
a) In order: 4%; 42%; 46%; 48%; 55%; 85% ✓M
The two middle values are 46% and 48% ✓M
Median = (46% + 48%) ÷ 2 ✓M = 47% ✓A
b) Netball, Hockey, Swimming, Tennis → 4 of the 6 ✓RT
P = ✓M = 0,667 ✓A
c) 42% of the total = 210 members
Total = 210 ÷ 42% ✓M = 500 members ✓A
d) Female = 500 − 210 ✓M = 290 members ✓A (or 58% × 500)
Difference = 290 − 210 ✓M = 80 members
The difference is 80 members, not 100 members, so the statement is NOT valid ✓O
Modelled on Nov 2025 Paper 1, Question 3.1 — same skills, new scenario.
Question 7
A provincial energy office recorded the number of rooftop solar installations (in hundreds) in its six districts from 2022 to 2024. The data is shown in the graph below. The 2024 segments of two districts have been left off the graph; their values are given in the table.
2024 INSTALLATIONS (IN HUNDREDS) THAT MUST STILL BE PLOTTED
| DISTRICT | 2024 |
|---|---|
| Eastern | 45 |
| Western | 35 |
- aWhat type of graph is this? (2)
- bWhich TWO districts had the same number of installations in 2022? (2)
- cDetermine the number of installations in the Southern district in 2023. Give your answer in hundreds, as on the graph. (3)
- dCalculate the range of the 2022 values of the 6 districts. Give your answer in hundreds, as on the graph. (4)
- eUse the table above to complete the graph for Eastern and Western. (On paper you would draw the two missing segments.) Write down the value on the vertical axis at which the top of EACH completed bar lies. (4)
- fOne of the 6 districts is chosen at random. Determine, as a fraction in simplified form, the probability that its TOTAL number of installations over the three years is less than 11 500 (that is 115 on the vertical axis). (2)
This question has a diagram, shown in the app.
Hint
In a stacked bar, a segment's value is the difference between the heights at which it ends and starts.
Worked answer
a) A compound (stacked) bar graph ✓✓A
b) Northern and Eastern ✓✓RG (both bottom segments end at 30)
c) The 2023 segment of Southern runs from 45 to 95 ✓RG
95 − 45 ✓M = 50 hundred ✓A (that is 5 000)
d) Highest = 55 (Central) ✓RG and lowest = 20 (Western) ✓RG
Range = 55 − 20 ✓M = 35 hundred ✓A (that is 3 500)
e) Eastern: 65 + 45 ✓M = 110 ✓A
Western: 50 + 35 ✓M = 85 ✓A
(See the completed graph below.)
f) Totals (tops of the completed bars, in hundreds): Northern 120; Southern 155; Eastern 110; Western 85; Central 185; Coastal 100
Below 115: Eastern, Western, Coastal → 3 of 6 ✓M
P = = ✓A
Modelled on Nov 2025 Paper 1, Question 3.2 — same skills, new scenario.
Question 8
A provincial department pays grants to early-childhood development (ECD) centres. The table below shows, per district, the number of centres that received a grant during 2024, the total amount paid and the average amount per centre. One average was left out.
GRANTS PAID TO ECD CENTRES PER DISTRICT
| DISTRICT | NUMBER OF CENTRES | TOTAL PAID (R million) | AVERAGE PER CENTRE |
|---|---|---|---|
| District 1 | 412 | 61,8 | R150 000 |
| District 2 | 268 | 37,5 | R139 925 |
| District 3 | 530 | 84,8 | R160 000 |
| District 4 | 196 | 25,5 | R130 102 |
| District 5 | 344 | 55,0 | R159 884 |
| District 6 | 287 | 40,2 | A |
| District 7 | 158 | 22,1 | R139 873 |
| District 8 | 465 | 72,1 | R155 054 |
| District 9 | 229 | 33,2 | R144 978 |
| District 10 | 371 | 53,8 | R145 013 |
| TOTAL | 3 260 | 486,0 |
- aCalculate the missing value A, the average grant per centre in District 6. Round your answer to the nearest thousand rand. (3)
- bWhich district has the third-largest number of centres? (2)
- cCalculate the mean amount (in R million) paid per district. (3)
- dWrite the numbers of centres in order, from the smallest to the largest. (2)
- eThe upper quartile (Q3) of the numbers of centres is 412. Calculate the interquartile range (IQR) of the numbers of centres. IQR = Q3 − Q1 (3)
Hint
R61,8 million is R61 800 000 — write the amount out in full before you divide by the number of centres.
Worked answer
a) R40,2 million = R40 200 000 ✓C
A = R40 200 000 ÷ 287 ✓M = R140 069,69
≈ R140 000 ✓R (to the nearest thousand rand)
b) District 1 ✓✓RT (largest counts: 530, 465, 412 → the third one belongs to District 1)
c) Mean = 486,0 ÷ 10 ✓RT ✓M
= R48,60 million ✓A
d) 158; 196; 229; 268; 287; 344; 371; 412; 465; 530 ✓✓A
e) Lower half: 158; 196; 229; 268; 287 → Q1 is its middle value = 229 ✓M
IQR = 412 − 229 ✓SF = 183 centres ✓A
Modelled on Nov 2025 Paper 1, Question 4.2 — same skills, new scenario.