IB Physics HLInquiry 2 — Collecting & Processing DataPractical Skillsaverages, uncertainties, sig figs~16 min read
Processing Data in Physics
This is the calculation phase — where your raw readings become the values that actually answer your research question. Processing means three things done carefully: averaging your repeat trials, propagating the uncertainty through every calculation, and presenting the results to the right number of significant figures. Do this cleanly and your graph almost draws itself.
📚 What you need to know
Average your repeat trials (excluding anomalies) before using a value further
Show one full worked example for every type of calculation you do
Add absolute uncertainties when adding or subtracting
Add fractional (or %) uncertainties when multiplying or dividing
Multiply the fractional uncertainty by the power when raising to a power
Quote your answer to the least precise number of significant figures used
Uncertainties get 1 significant figure; match the answer’s decimal places to it
Start with the average
When you have repeat trials, the first move is to calculate the mean — but only after throwing out any clearly anomalous result. That averaged value is what feeds into the rest of your calculations.
Averaging isn’t just tidying up — it’s what makes your result reliable. Random wobbles in individual readings partly cancel when you take a mean, so the average is closer to the true value than any single trial. Just remember to drop the outlier first, or it drags the mean off with it.
Propagating uncertainties
Every raw measurement carries an uncertainty, and when you push those measurements through a calculation, the uncertainty travels with them. Three rules cover almost every situation you’ll meet.
Match the rule to the operation: add absolutes for ±, add fractions for × and ÷, and multiply the fraction by the power.
Worked example: a period (divide by an exact number)
WE 1
A pendulum is timed for 20 oscillations three times: 28.4 s, 28.6 s, 28.5 s, each ±0.2 s. Find the period T of one oscillation and its absolute uncertainty.
Step 1 — average the trialst20 = (28.4 + 28.6 + 28.5) / 3 = 28.5 sStep 2 — period (divide by exact 20)T = 28.5 / 20 = 1.425 s → 1.43 s (3 s.f.)Step 3 — % uncertainty (20 is exact, adds nothing)
(0.2 / 28.5) × 100 = 0.70%Step 4 — back to absolute
ΔT = 0.0070 × 1.425 = 0.01 sT = 1.43 ± 0.01 sDividing by an exact number (like the count 20) doesn’t change the % uncertainty — it has no uncertainty of its own.
Worked example: a resistance (divide, add fractions)
WE 2
A wire carries current I = 1.24 ± 0.01 A under a potential difference V = 1.68 ± 0.01 V. Find its resistance R and the absolute uncertainty, using R = V / I.
Step 1 — the resistanceR = 1.68 / 1.24 = 1.35 Ω (3 s.f.)Step 2 — add the % uncertainties (division)
(0.01/1.68)×100 + (0.01/1.24)×100 = 0.60% + 0.81% = 1.41%Step 3 — convert back to absolute
ΔR = 0.0141 × 1.35 = 0.02 Ω (1 s.f.)R = 1.35 ± 0.02 ΩFor a divide, add the percentages first, then turn the total back into an absolute ± on the final answer.
Worked example: kinetic energy (a power)
WE 3
A trolley of mass m = 0.150 ± 0.002 kg moves at v = 2.40 ± 0.05 m s−1. Find its kinetic energy Ek = ½mv² and the percentage uncertainty.
Step 1 — the energyEk = ½ × 0.150 × 2.40² = 0.432 JStep 2 — combine % uncertainties (v is squared → ×2)
% in m = 1.33%, % in v = 2.08%
% in Ek = 1.33 + 2×2.08 = 5.5%Ek = 0.432 J ± 5.5%Because v is squared, its percentage uncertainty counts twice — that’s the power rule doing its job.
Significant figures and presenting your data
Your final answer should carry the same number of significant figures as the least precise piece of raw data used to get it. Writing down the full calculator display is a giveaway that you’ve lost track of precision.
💡 Top tips
Round the uncertainty to 1 significant figure first, then match the answer to it.
Match the answer’s decimal places to its absolute uncertainty (1.43 ± 0.01, not 1.4 ± 0.01).
Show one full worked example per calculation type — even if a spreadsheet did the rest.
Present raw and processed data in the same clearly labelled table, with a numbered title.
Linearising to a straight line
Many physics relationships are curves, and curves are hard to read precisely. The trick is to linearise: rearrange the known formula so a graph of the right quantities gives a straight line. For a pendulum, the period relates to length by:
Pendulum — rearranged to linear formT = 2π√(L / g) → T² = (4π² / g) L
Compare that to the equation of a straight line, y = mx + c. Plotting T² on the y-axis against L on the x-axis gives a straight line through the origin, with gradient 4π² / g.
Curve T vs L
rearrange the formula
Straight line T² vs L
read the gradient
Find g
Why bother turning a nice curve into a boring straight line? Because a straight line hands you two gifts: its gradient and its intercept, both of which usually equal a real physical quantity you’re after. A curve hides that information; a straight line lays it out in the open. You’ll cash this in on the next page when we read a graph.
⚠ Common mistakes
Adding absolute uncertainties when multiplying or dividing (add fractions).
Forgetting to ×2 (or ×n) the fractional uncertainty for a squared/powered term.
Quoting the full calculator display instead of sensible significant figures.
Rounding the uncertainty to more than 1 significant figure.
Including an anomaly in the average.
Quick recap:Average trials (drop anomalies). Propagate uncertainty: add absolutes for ±, add fractions for ×÷, ×n for powers. Uncertainty to 1 s.f., answer’s decimals matched to it. Linearise a curve so a straight-line graph reveals the gradient you need.
Your data is now processed: clean averages, honest uncertainties, and a plan to plot a straight line. The final step is to make sense of it — to look at the graph and say what the physics is actually doing. That’s the job on Interpreting Results in Physics, where gradients, intercepts, and the words accuracy and precision all come together.
Uncertainties still tripping you up?
Book a free meeting and we’ll drill averaging, propagating uncertainties, and linearising graphs until they feel automatic — the processing skills that carry marks across every IA and Paper 3.
