Numbers are useful only when they answer a clear question. A school colour-indicator exhibition can generate volumes, ratios, records and graphs, yet a correct calculation may still produce a misleading claim if its denominator is wrong or the underlying observation does not measure what the speaker says it measures. G3 Mathematics asks learners to recognise the structure beneath a story, choose an appropriate operation, carry it out accurately and interpret the result within its limits.
This guide uses invented records from a teacher-prepared red-cabbage indicator display. There is no need to prepare substances or perform any unsupervised chemical work. The colours are qualitative categories, not pH values: naming pink, purple or green cannot turn an arbitrary colour code into a measured hydrogen-ion concentration. Throughout, the calculations apply to volumes of prepared liquids, frequencies of observations, numerical reference measurements and constraints. None of the example values represent data from a real Sengkang school.
- First build secure number foundations: part-to-part and part-to-whole ratios, fractions, decimals, percentages and units.
- Then interpret records: frequencies, averages of numerical measurements, intervals, graphs, inconsistent data and sample sizes.
- Finally make examination decisions: check constraints, justify what the mathematics proves and distinguish a calculation from an unsupported scientific claim.
Why this is the next learner’s guide
Vol 0973 Chemistry Red-Cabbage Indicator established how to describe a colour response fairly. We now study the mathematics of that record without taking ownership of chemical identity, purity or safety claims. Read the G3 Mathematics preparation route for progression from Secondary 1, or the PSLE Mathematics error-diagnosis guide if you need a simpler way to discover whether an error came from representation, method or decision.
The official 2027 examination framework
The official SEAB directory lists 2027 G3 Mathematics as K310. The 2027 K310 syllabus specifies Paper 1 and Paper 2, each lasting 2 hours 15 minutes and each carrying 90 marks or 50% of the examination. Consult the syllabus for the definitive content, formula, calculator and presentation requirements. The indicator exhibition is a fresh example of mathematical reasoning, not a prescribed examination experiment.
A strong Paper 1 or Paper 2 student does more than apply a formula. For a ratio, ask what the two quantities represent. For a percentage, identify its base. For an average, decide whether the values can legitimately be averaged. For a graph, look at the variable types and axes. For a model, test whether its output satisfies the conditions. An answer can be arithmetically flawless yet conceptually invalid if it uses colour categories as precise pH readings or extrapolates a few trials to a city-wide claim.
One model record: know what the columns mean
A worksheet has columns for code, pre-measured sample volume in millilitres, pre-measured indicator volume in millilitres, combined nominal volume in millilitres, observation time in seconds and response colour. These fields do not carry equal mathematical meaning. Volumes and times are numerical measurements with units. The colour is a categorical observation. The code is an identifier. A number such as 2026 in a sample code is not a quantity to average. This classification is the first protection against attractive nonsense.
Imagine Cup A contains 18 mL prepared sample and 3 mL prepared indicator: its nominal total is 21 mL, assuming no specified loss or contraction. The part-to-part ratio is 18:3 or 6:1. Its indicator fraction of the whole is 3/21 or 1/7, approximately 14.3%. These are three related statements with three different forms. If you wrote ‘3/18 is 14.3%’ you would have confused a part-to-part quotient with a part-to-whole proportion. The habit to learn is to draw the whole before dividing.
In a two-batch trial, a statistic may be expressed as a frequency, a within-batch percentage or a share of all planned tests. Each answers a different question. A missing record can change the denominator; repeated observations can introduce dependence; an uneven group size can invalidate the plain average of percentages. Before calculating, underline the population, the event and the comparison named by the question.
Detailed worked cases: move from arithmetic to inference
Worked case 01. Total volume
Question. 15 mL sample plus 5 mL indicator. Find or evaluate the quantity named.
Solution. 20 mL nominal total; 15+5=20. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. State the assumption of no specified loss; do not silently rewrite an observed total if a question records a discrepancy. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 02. Part-to-whole percentage
Question. Five of 20 mL come from indicator. Find or evaluate the quantity named.
Solution. 5/20×100%=25%. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Using 5/15 would answer indicator relative to sample, not indicator as a share of the mixture. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 03. Ratio simplification
Question. 18 mL sample and 3 mL indicator. Find or evaluate the quantity named.
Solution. 18:3 simplifies to 6:1. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. The denominator for a mixture fraction instead has seven equal parts; distinguish notation from meaning. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 04. Missing mixture component
Question. Total 32 mL, sample:indicator=7:1. Find or evaluate the quantity named.
Solution. Eight equal parts make 4 mL each; indicator 4 mL and sample 28 mL. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Check 28+4=32 and 28/4=7, because a plausible-looking quantity can violate one of the two conditions. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 05. Linear equation
Question. Indicator x mL, sample 3x+2 mL, total 22 mL. Find or evaluate the quantity named.
Solution. x+(3x+2)=22, so x=5 mL and sample 17 mL. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. A solved x is not necessarily the requested quantity; reread the final instruction. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 06. Increase percentage
Question. A reference changes from 4 mL to 5 mL. Find or evaluate the quantity named.
Solution. Difference 1 mL; 1/4×100%=25% increase. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. The old amount is the base for percentage increase, not the new 5 mL. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 07. Decrease percentage
Question. A numerical instrument changes from 25 to 20 arbitrary units. Find or evaluate the quantity named.
Solution. Difference 5, so 5/25×100%=20% decrease. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. This describes the instrument’s reading. It does not prove a chemical became 20% less acidic. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 08. Percentage points
Question. Category share rises from 35% to 50%. Find or evaluate the quantity named.
Solution. It rises by 15 percentage points. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Relative percentage increase would be 15/35≈42.9%, a different statement with a different denominator. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 09. Frequency and fraction
Question. Twenty-four observations: 9 pink, 11 purple, 4 green. Find or evaluate the quantity named.
Solution. Total 24; purple share 11/24≈45.8%. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. It is the observed proportion of one colour class, not an independently established proportion of neutral chemicals. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 10. Small population
Question. Three pink results among four prepared cups. Find or evaluate the quantity named.
Solution. 3/4=75% within this sample. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. A leaflet cannot infer that 75% of all water is acidic. A within-sample count does not establish representativeness. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 11. Missing observations
Question. Thirty trials planned; 27 recorded; 15 of those purple. Find or evaluate the quantity named.
Solution. Observed share 15/27≈55.6%. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. If asked the fraction confirmed among planned trials, 15/30=50%; tell the reader which denominator was selected. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 12. Frequency table
Question. Sequence: P,P,U,G,U,U,G,P,U,U, with P pink, U purple and G green. Find or evaluate the quantity named.
Solution. P=3, U=5, G=2; sum 10. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. A short frequency table also gives a built-in check: its counts must equal the number of entries. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 13. Modal category
Question. The ten-observation table has counts 3,5,2. Find or evaluate the quantity named.
Solution. Purple is the modal category. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Mode is appropriate for nominal categories; a mean colour is not meaningful without a genuine numerical scale. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 14. Arbitrary colour codes
Question. Pink=1, purple=2, green=3 are labels in a spreadsheet. Find or evaluate the quantity named.
Solution. Do not call their mean a pH value. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. The coding system was chosen for convenience; its distances have no calibrated chemical or numerical meaning. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 15. Misleading bar axis
Question. A bar chart of counts 9,10,11 begins its vertical scale at 8. Find or evaluate the quantity named.
Solution. The bar-length differences appear exaggerated. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Explain how a zero baseline can make absolute frequency comparisons more intelligible; identify any intentional exception. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 16. Unequal group sizes
Question. Group A: 8 pink in 10; B:15 pink in 25. Find or evaluate the quantity named.
Solution. A=80%, B=60%. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. The larger raw count for B conceals a smaller within-group percentage. Compare the same statistic. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 17. Weighted percentage
Question. Combine A’s 8/10 and B’s 15/25. Find or evaluate the quantity named.
Solution. 23 pink out of 35, or ≈65.7%. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Do not simply average 80% and 60% as 70%: the groups have unequal sample sizes. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 18. Rounding
Question. Calculate 17/30×100%. Find or evaluate the quantity named.
Solution. 56.666…%; 56.7% to one decimal or 57% to whole percent. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Keep intermediate precision and obey the requested form; rounded intermediates accumulate error. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 19. Mean of numerical readings
Question. A valid meter dataset: 6.8,7.0,6.9,7.1. Find or evaluate the quantity named.
Solution. Mean=(6.8+7.0+6.9+7.1)/4=6.95. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. This is a mean of numerical meter readings, not a mean of observed red-cabbage colours. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 20. Range
Question. Use numerical readings 6.8,7.0,6.9,7.1. Find or evaluate the quantity named.
Solution. Range=7.1−6.8=0.3. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. A small range shows close clustering but does not rule out a shared instrument calibration bias. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 21. Median with outlier
Question. Readings 6.8,6.9,7.0,7.1,9.6. Find or evaluate the quantity named.
Solution. Median is 7.0; mean is 37.4/5=7.48. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. An extreme reading can pull the mean; do not delete it without explaining a justified data-quality decision. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 22. Fraction constraint
Question. 16 mL sample; indicator x at most 20% of total. Find or evaluate the quantity named.
Solution. x/(16+x)≤0.2 gives x≤4 mL. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. A simple 20% of 16 gives 3.2 mL, but the added indicator is part of the total denominator. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 23. Integer feasibility
Question. Dispenses in whole millilitres, permitted x≤4 mL. Find or evaluate the quantity named.
Solution. The maximum permitted integer is 4. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. For a ceiling of 4.6 mL, round downward, not to nearest 5; feasibility outranks conventional rounding. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 24. Interval rate
Question. 12 readings by minute 4; 27 readings by minute 10. Find or evaluate the quantity named.
Solution. (27−12)/(10−4)=15/6=2.5 readings per minute. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. This is a processing rate, not chemical reaction rate; keep the unit and meaning in view. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 25. Unit test
Question. A student subtracts 3 readings per minute from 20 mL. Find or evaluate the quantity named.
Solution. The operation has no direct physical meaning. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Quantities with incompatible dimensions cannot be combined by ordinary subtraction without an appropriate relationship. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 26. Percentage error
Question. Reference 20.0 mL, reading 19.5 mL. Find or evaluate the quantity named.
Solution. Absolute error 0.5 mL; percent error 0.5/20.0×100%=2.5%. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Use the designated reference as denominator. Error percentage does not prove the underlying chemical method is valid. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 27. Graph selection
Question. Categorical colour for each cup and numeric mixture volume. Find or evaluate the quantity named.
Solution. Bar chart for colour frequencies; numeric scatter plot only for an appropriate pair of numerical variables. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Do not draw a continuous line joining unordered colour labels; its slope would imply a false numeric order. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 28. Valid labels
Question. A plot shows frequencies but no title or vertical-axis unit. Find or evaluate the quantity named.
Solution. Add a descriptive title and label the count axis ‘number of observations’. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Precise labels protect the interpretation: a frequency is not the same thing as a percentage or a measured pH. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 29. Reliability versus validity
Question. Two groups get consistent observations using different indicator batches. Find or evaluate the quantity named.
Solution. Consistent repeats can show internal repeatability, not necessarily comparability between groups. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. If the measurement process changes, the numerical analysis must state the limitation rather than assume full equivalence. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 30. Out-of-range percentage
Question. A solution claims 26 positive cases out of 20 total =130%. Find or evaluate the quantity named.
Solution. Recheck counts and denominator; a subset cannot exceed its total. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. A rapid bounding check can catch transcription errors that a calculator will reproduce faithfully. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 31. Target budget
Question. Thirty display cups each require 4 mL indicator; stock has 110 mL. Find or evaluate the quantity named.
Solution. Required 30×4=120 mL, a shortfall of 10 mL. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. The plan is infeasible as stated. A correct solution must report insufficiency, not merely the calculated demand. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 32. Alternative plan
Question. With 110 mL stock and 4 mL per cup, whole cups only. Find or evaluate the quantity named.
Solution. 110/4=27.5, so at most 27 complete cups; 2 mL remains. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. An answer of 27.5 cups is mathematically a quotient but not an implementable count of complete prepared cups. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 33. Sampling bias
Question. A class reports only the clearest 12 readings from 20 prepared samples. Find or evaluate the quantity named.
Solution. The reported 12 may be selected for visibility and need not represent all 20. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Explain the selection mechanism. Averaging or graphing the selected data cannot remove the missingness bias. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
Worked case 34. A claim about precision
Question. A result is shown as 48.273%, but only 20 categorical trials were recorded. Find or evaluate the quantity named.
Solution. The count resolution is in steps of 5 percentage points. Show the intermediate step and ensure the result answers the question, rather than a nearby but different question.
Examination insight. Extra decimal places cannot create information not present in the observations; an appropriate percentage expresses count and sample size. When you review this solution, identify the data type, the denominator or reference, the units and the strength of the conclusion. This extra check is worth practising because real examination questions often embed the arithmetic inside a claim that itself needs evaluation.
One extended interpretation task
A fictional exhibit reports Batch One: 12 trials, 7 pink, 4 purple and 1 green. Batch Two: 18 trials, 6 pink, 9 purple and 3 green. The combined count is 30, with 13 pink, 13 purple and 4 green. Pink and purple are joint modal categories, each appearing in 13/30 of the observations, about 43.3%. The figures describe what was recorded from these specific prepared samples and do not establish an environmental or drinking-water conclusion.
Compare within groups to reveal a different view. Batch One’s purple share is 4/12=33.3%, while Batch Two’s is 9/18=50%. This is approximately 16.7 percentage points higher in Batch Two. It is not a difference of 16.7 pH units; pH was not measured numerically by this categorical display. If the samples were chosen or recorded in different ways, even the comparative percentage needs a careful explanation of its limits. The distinction between accurate calculation and warranted inference is the heart of mathematical literacy.
Now imagine that two Batch Two labels may be wrong. We cannot repair their categories by guessing. If a question asks for a revised percentage without identifying the mislabelled observations, an appropriate response is that the exact revision is underdetermined. If it gives conditions for their possible classifications, construct upper and lower bounds. This method is often stronger than inserting a fabricated ‘best estimate’ and pretending the uncertainty has disappeared.
How to write efficient, mark-worthy solutions
First express what the symbol stands for. A line such as ‘Let x be the indicator volume in mL’ makes the following inequality readable. Second, keep the relationship visible before substituting numbers. Third, check units, signs and size. Fourth, substitute the proposed answer into the original condition. Fifth, attach an interpretation with an appropriate scope. Every line should do a job. If you cannot say why a line exists, it may be unnecessary.
For multiple-choice questions, eliminate impossible answers before doing full arithmetic. A percentage of a subset cannot exceed 100% when the count and denominator represent the same population. A negative volume is not a usable solution. A mean must lie between the smallest and largest observations in the dataset, unless you have combined different transformations or made a mistake. These quick checks build speed without sacrificing the reasoning needed in longer structured questions.
For extended Paper 2 work, favour a compact layout: a labelled table where helpful, an algebraic or numerical line, a clear equality or inequality, and one sentence interpreting it. Do not write sprawling prose instead of mathematics. Yet do not omit the interpretation when the command asks whether a recommendation is valid. The last sentence is often the difference between calculating a number and answering the examination question.
A seven-day revision sequence
Day one is for ratio structures: part-to-part, part-to-whole, simplifying and scaling. Day two is for percentage increase, decrease and percentage-point change. Day three is for frequency tables and graph choice. Day four is for uneven group sizes and weighted overall rates. Day five is for mean, median, range, unusual readings and the difference between accuracy and precision. Day six is for equations, inequalities, feasible integer solutions and unit checks. Day seven is for a timed unseen data task in which you must write an explicit conclusion supported by the calculated result.
After each session, classify the first error rather than just marking the final answer wrong. Was the quantity misunderstood? Was the representation incorrect? Was the operation poorly chosen? Did the arithmetic slip? Did the final claim outrun the result? Repair only that link, then attempt a new short question. This approach is especially helpful to students coming from PSLE who are learning to make their mathematical working visible to another reader.
Questions from learners and parents
Can we calculate a mean of red-cabbage colours?
Not by assigning arbitrary numbers to names. A mean requires meaningful numerical measurements. You can, however, count each category, find its proportion and determine the modal response.
Is a weighted percentage always difficult?
No. For an overall percentage across groups, add relevant successes and add relevant totals before dividing. The difficult part is resisting the tempting but wrong average of unequal group percentages.
When should I round?
Normally keep adequate accuracy in intermediate calculations and round the final result to the form requested. When a real-world constraint requires a whole number, apply a feasible rounding direction rather than blindly rounding to nearest.
How do I know whether a graph is honest?
Ask whether its axes are labelled, its scale is appropriate, its quantities are comparable, its data type fits the chart, and its headline describes only the results actually represented.
Where the series goes next
Vol 0975 uses these records as source material for English Paper 1: write a clear exhibition notice, preserve the numerical qualifications and give the audience an accurate safety message. Vol 0976 will combine the scientific and mathematical evidence into a final public claim review. If volume and denominator errors are still troublesome, revisit Vol 0966, Mathematics Water-Filter Trials for a different context that tests the same habit of reconciling what comes in and what goes out.
The durable lesson is to calculate the quantity asked for and then say exactly what that number can, and cannot, demonstrate.
