Two students time the same reaction and get 24 seconds and 31 seconds. Neither is lying and neither made a "silly mistake" — real measurements always carry some uncertainty, and real results always scatter a little. Knowing how to handle that scatter honestly is what turns raw numbers into science you can trust.
Choosing apparatus and units
Take an investigation into how the concentration of hydrochloric acid affects the rate of reaction with magnesium ribbon, measuring the volume of hydrogen gas produced using a gas syringe. The apparatus you choose must match the precision you need: a gas syringe reads to the nearest cm³, far more precise than trying to judge a rough volume by eye. Units must always be recorded and must be appropriate — volume in cm³, mass in g, time in s, temperature in °C. Choosing a measuring cylinder with too big a range (say 0–250 cm³ for measuring 5 cm³ of liquid) throws away precision you could easily have kept by choosing a smaller one.
Repeating measurements and calculating a mean
A single reading could be a fluke. Repeating the experiment — usually at least three times — for each value of the independent variable lets you calculate a mean (average), which is far more reliable than any single reading, because random errors in individual trials tend to cancel out.
| Concentration (mol/dm³) | Repeat 1 (s) | Repeat 2 (s) | Repeat 3 (s) | Mean (s) |
|---|---|---|---|---|
| 0.5 | 48 | 51 | 49 | 49.3 |
| 1.0 | 24 | 41 | 23 | 23.5* |
| 2.0 | 12 | 13 | 11 | 12.0 |
*Repeat 2 at 1.0 mol/dm³ (41 s) does not fit the pattern of the other two repeats at that concentration — it is an anomalous result. Because it is so different from the other repeats at the same concentration, it should be identified, investigated if possible (was there a leak? was the stopwatch started late?) and repeated — not simply averaged in as if it were a normal reading, and not silently deleted without comment either. Once a genuine anomaly is confirmed, it is excluded and the mean is calculated from the remaining, consistent repeats: (24 + 23) ÷ 2 = 23.5 s.
Measurement uncertainty
No measurement is ever perfectly exact — every instrument has a resolution (the smallest change it can detect), and this limits how precisely you can know a value. A measuring cylinder marked in 1 cm³ divisions can typically only be trusted to within ±0.5 cm³ (half the smallest division) — so a reading of "24 cm³" should really be recorded and thought of as "24 ± 0.5 cm³". Recording uncertainty honestly, rather than pretending a reading is exact, is a mark of good scientific practice.
Presenting results: table, then graph
Raw data always goes into a clear table first, with headings and units in the top row. To display it visually, choose the graph type that matches the data:
- Line graph — use when the independent variable is continuous (any numerical value is possible), such as concentration, temperature or time. Plot points and draw a single best-fit line or smooth curve.
- Bar chart — use when the independent variable is categoric (separate, distinct categories), such as different metals, different enzymes, or different countries. Bars should not touch.
Put these steps of a scientific investigation in the correct order:
- Record raw repeat readings in a table with headings and units
- Check for anomalous results and repeat any that don't fit the pattern
- Calculate the mean of the consistent repeats
- Plot the means on an appropriately chosen graph
- Draw a conclusion linking the pattern to the independent variable
- Evaluate the method: identify a limitation and suggest a genuine improvement
Evaluating a method
Evaluating means honestly judging how good the method was, after the results are in. A weak evaluation just says "human error" — this explains nothing. A strong evaluation names a specific, real limitation of the method, such as: "gas escaped during the short time it took to connect the syringe after the reaction started, so measured volumes were probably all slight underestimates," and then suggests a genuine improvement that would fix that exact problem, such as: "use a bung with the syringe already attached, or a delivery tube sealed with the reaction vessel from the very start, so no gas can escape before timing begins."
(a) 38 s does not fit the pattern of 15 s and 16 s. (b) They should try to repeat that specific reading rather than simply averaging all three or deleting it silently; if a repeat confirms 15–16 s is typical, the mean should be calculated from 15 s and 16 s only (15.5 s), and the 38 s reading noted as excluded with a reason. (c) A plausible specific cause: the stopwatch may have been started a few seconds late, or the solutions may not have been mixed as thoroughly that time — not simply "a mistake was made".
Memory hook: repeat, spot the odd one out, then mean the rest — never average away an anomaly without questioning it first. And an evaluation is only worth marks when it names a real, specific limitation and a real, specific fix — not "try harder next time".