IB Chemistry HLInquiry 2 — Collecting and Processing DataPaper 3 & IACore skill~13 min read
Processing Data
Now the numbers have to become an answer. This is the stage students rush, and it is the stage that separates a decent investigation from a strong one — because processing is not just getting a value, it is knowing how much to trust it.
📘 What you need to know
Processed data goes in a separate, clearly titled table from your raw data.
Average only concordant results — titres within 0.10 cm3 of each other. The rough run and any anomaly are left out.
Show one full worked calculation for every type of processing you did, even if a spreadsheet did the rest.
Adding or subtracting → add the absolute uncertainties.
Multiplying or dividing → add the percentage uncertainties.
Raising to a power → multiply the percentage uncertainty by that power.
Quote the uncertainty to one significant figure, and round the answer to match its decimal place.
Two tables, not one
Your raw data table shows what you measured. Your processed table shows what you worked out from it. Keeping them apart is not fussiness — it lets the examiner check your arithmetic against your measurements, which is exactly what they want to do.
A processed table for a titration might have columns for the mean titre, the moles of titrant, the moles of the unknown, and the final concentration. Every one of those came out of a calculator, so none of them belong in the first table.
Average only what deserves averaging
The rough run exists to find roughly where the endpoint is. It was run fast, it overshot, and it is not a measurement of anything. Leave it out.
After that, keep the titres that agree within 0.10 cm3. Those are your concordant results, and they are the only ones you average. If only two agree, run another titration rather than averaging in one that clearly does not fit.
An extra check worth doing: half the range of your concordant results, (max − min) ÷ 2, is a rough uncertainty on the mean. If it comes out bigger than your instrument uncertainty, your repeats are scattering more than the burette can explain — and you should quote the bigger value.
Carrying the uncertainty through
Two rules cover almost everything you will meet. Which one applies depends only on the arithmetic you just did.
A third rule for HL: if you raise a quantity to a power, multiply its percentage uncertainty by that power. Squaring something doubles the percentage uncertainty.
🧩 Propagating uncertainty, step by step
Start with each raw measurement and its absolute uncertainty, straight from your table headers.
Do any subtractions first — titres, mass by difference, temperature rise — adding the absolutes as you go.
Convert each one to a percentage before you multiply or divide anything.
Add the percentages through the rest of the calculation.
Convert back to an absolute at the very end: final answer × total % ÷ 100.
WORKED EXAMPLE
Processing a titration all the way to an answer with uncertainty
25.00 ± 0.03 cm3 of an iron(II) solution is titrated with 0.0200 mol dm–3 KMnO4. Titres: rough 22.10, then 21.35, 21.40 and 21.30 cm3 (each ±0.10). The equation is MnO4– + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O. Find the concentration of Fe2+.
Step 1: Pick the concordant titres and average them
Rough excluded. Range of the other three = 0.10, so all three are concordant.
mean = (21.35 + 21.40 + 21.30) ÷ 3 = 21.35 cm³Step 2: Moles of MnO₄⁻n = 0.0200 × 21.35 ÷ 1000 = 4.270 × 10⁻⁴ molStep 3: Use the ratio — 1 MnO₄⁻ reacts with 5 Fe²⁺n(Fe²⁺) = 5 × 4.270 × 10⁻⁴ = 2.135 × 10⁻³ molStep 4: Divide by the pipetted volume in dm³c = 2.135 × 10⁻³ ÷ 0.02500 = 0.0854 mol dm⁻³Step 5: Add the percentage uncertainties
Burette: 0.10 ÷ 21.35 × 100 = 0.47%
Pipette: 0.03 ÷ 25.00 × 100 = 0.12%
total = 0.59% → 0.0854 × 0.0059 = 0.0005c(Fe²⁺) = 0.0854 ± 0.0005 mol dm⁻³the 5:1 ratio is exact, so it adds no uncertainty at all
Which measurement is dragging you down?
Once you have those percentages, do not throw them away. They tell you exactly which piece of apparatus is limiting your whole investigation — and that is the single most useful thing you can put in an evaluation.
With a pipette, the burette dominates — so a wider titre or a finer burette is the improvement worth suggesting. Nothing you do to the pipette will matter much.
WORKED EXAMPLE
A rate, with two uncertainties feeding into it
A gas syringe collects 18.5 ± 0.5 cm3 of hydrogen in 30.0 ± 0.2 s. Find the rate and its uncertainty, and say which measurement is worth improving.
Step 1: The rate itselfrate = 18.5 ÷ 30.0 = 0.6167 cm³ s⁻¹Step 2: Percentage uncertainty in each measurementvolume: 0.5 ÷ 18.5 × 100 = 2.70%time: 0.2 ÷ 30.0 × 100 = 0.67%Step 3: It is a division, so add the percentagestotal = 3.37%Step 4: Back to an absolute uncertainty0.6167 × 0.0337 = 0.0208 → 0.02rate = 0.62 ± 0.02 cm³ s⁻¹the volume contributes four times as much as the time — collect for longer, do not buy a better stopwatch
Significant figures and how to quote the answer
Your calculator will happily give you ten digits. Almost all of them are lies. The rule is simple: your answer can be no more precise than the least precise measurement that went into it.
Situation
What to do
Example
Multiplying or dividing measurements
Match the fewest significant figures used
0.0200 (3 s.f.) and 21.35 (4 s.f.) → answer to 3 s.f.
Adding or subtracting
Match the fewest decimal places
21.50 − 0.15 = 21.35, all to 2 d.p.
Quoting the uncertainty
Round it to 1 significant figure
0.000503 → 0.0005
Quoting the final value
Round it to the same decimal place as the uncertainty
0.08540 ± 0.0005 → 0.0854 ± 0.0005
Exact numbers (ratios, 1000, ×10 dilutions)
Ignore them — they carry no uncertainty
The 5:1 ratio adds nothing
WORKED EXAMPLE
Rounding a messy calculator answer sensibly
A calculation gives a concentration of 0.0854013 mol dm–3 with a total percentage uncertainty of 0.59%. Write down the final answer properly.
Step 1: Work out the absolute uncertainty first0.0854013 × 0.0059 = 0.000504Step 2: Round the uncertainty to 1 s.f.0.000504 → 0.0005Step 3: Round the value to the same decimal place
The uncertainty sits in the fourth decimal place, so the value stops there too.
0.0854013 → 0.0854Step 4: Sanity check against the raw data
Least precise raw value was 3 s.f., and 0.0854 is 3 s.f. Consistent.
0.0854 ± 0.0005 mol dm⁻³work out the uncertainty first — it tells you where to stop rounding
💡 Exam tip
Show one full worked example of each calculation type. A spreadsheet full of numbers with no visible method scores badly.
Write the units of every processed column, including derived ones like cm3 s–1 or mol dm–3 s–1.
Do subtractions in absolutes, then switch to percentages. Doing it the other way round gives the wrong answer.
Ratios from a balanced equation are exact. They never add uncertainty.
Keep full precision through the middle of a calculation and round only at the end — rounding early accumulates error.
If your percentage uncertainty comes out above about 10%, say so and explain which measurement caused it.
⚠ Common mix-up
Adding percentages for a subtraction. Subtractions use absolutes.
Averaging the rough titre in with the accurate ones.
Forgetting the mole ratio. With MnO4– and Fe2+ it is 1:5, and skipping it makes your answer five times too small.
Copying the whole calculator display into the table.
Quoting the uncertainty to 3 s.f. One significant figure is enough — you do not know it that well.
Rounding partway through and carrying the rounded value forward.
Leaving processed values in the raw data table. They belong in their own table with a title.
Up next: Interpreting Results — turning that processed table into a graph, describing the trend properly, and explaining it with actual chemistry.
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