Random vs Systematic Errors

Every measurement is a little bit wrong. The important question isn’t whether errors exist, but what kind they are, because the two main types of error behave completely differently. One kind scatters your results randomly and can be tamed by repeating. The other kind shifts every result in the same direction, and no amount of repeating will reveal it. Knowing the difference is essential for evaluating experiments well.

The definitions

Random errors cause measurements to vary unpredictably around the true value, sometimes too high, sometimes too low.

Systematic errors cause measurements to be consistently too high or too low by a similar amount (or proportion) every time.

Side-by-side comparison

	Random error	Systematic error
Direction	varies: sometimes high, sometimes low	always the same direction
Effect on repeated results	scatter (spread)	consistent shift (bias)
Affects mainly	precision	accuracy
Reduced by repeating and averaging?	yes	no
How to detect	spread of repeat results	comparing with an accepted value or a different method
How to reduce	repeats, better technique, more precise instruments	calibration, better method, correcting the cause
Typical causes	reading judgement, fluctuating conditions, reaction time	faulty or uncalibrated equipment, flawed method, heat loss

The target analogy

Imagine throwing darts at a target, where the bullseye is the true value:

• Low random error, low systematic error: darts tightly grouped on the bullseye. Accurate and precise.
• High random error, low systematic error: darts scattered widely, but centred on the bullseye. Accurate on average, not precise.
• Low random error, high systematic error: darts tightly grouped, but off to one side. Precise, not accurate.
• High random error, high systematic error: darts scattered and off-centre. Neither.

The dangerous case is the third one. Tightly grouped results feel trustworthy, but they can all be wrong in the same way.

Examples of random errors in chemistry

• Judging an end point in a titration: stopping a fraction of a drop early one time and late the next.
• Reading a scale between marks on a thermometer or measuring cylinder.
• Human reaction time when starting and stopping a stopwatch.
• Small fluctuations in room temperature, draughts on a balance, or electrical noise in an instrument.
• Judging when a cross disappears in the sodium thiosulfate experiment.

Examples of systematic errors in chemistry

• An uncalibrated balance that always reads 0.02 g too high.
• A thermometer whose scale is offset by 1 °C.
• Heat lost to the surroundings in calorimetry: the measured temperature rise is always too small, so energy changes are always underestimated.
• Not rinsing a burette with the titrant: the titrant is diluted, so every titre is too large. See common titration errors.
• Reading the top of the meniscus instead of the bottom, consistently.
• A reaction that doesn’t go to completion, or gas escaping before the bung is replaced, consistently reducing the measured amount of product.
• Sodium hydroxide that has absorbed CO₂, making its true concentration lower than the label says.
• Parallax error, if you always read from the same wrong angle.

Spotting them in data

Random error shows up as scatter:

• repeats differ from one another
• points scatter above and below a line of best fit

Systematic error is harder to spot because the results can look perfectly consistent. Clues include:

• the mean result differs from a known accepted value by more than the experimental uncertainty
• a calibration line that should pass through the origin has a clear intercept (a zero error)
• results change when a different method or instrument is used

A useful check: compare the percentage error (difference from the accepted value) with the percentage uncertainty of your measurements. If the error is much bigger than the uncertainty, there’s probably a systematic error. See calculating percentage uncertainty.

Zero errors: a special systematic error

A zero error happens when an instrument doesn’t read zero when it should: a balance showing 0.03 g with nothing on it, or a meter that reads slightly off with no input. Every reading is shifted by the same amount. The fix is simple: tare or zero the instrument before use, or subtract the offset from every reading.

Reducing each type

Random errors:

1. Repeat measurements and calculate a mean.
2. Use more precise instruments (e.g. a burette instead of a measuring cylinder, a digital thermometer reading to 0.1 °C).
3. Improve technique: read at eye level, swirl consistently, use a white tile for colour changes.
4. Use automated measurement (data loggers, light sensors) to remove human judgement.
5. Measure larger quantities, so fixed reading errors are a smaller fraction.

Systematic errors:

1. Calibrate instruments against standards (buffers for pH meters, reference masses for balances).
2. Zero or tare instruments before use.
3. Improve the method to remove the cause: insulate a calorimeter and use a lid; rinse the burette properly; standardise solutions.
4. Use a different method to cross-check the result.
5. Correct mathematically where the size of the error is known, for example extrapolating a cooling curve to correct for heat loss.

Writing about errors in an evaluation

Examiners reward evaluations that are specific. For each error, say:

1. What the error is.
2. Whether it’s random or systematic.
3. Its effect on the result (too high or too low, or more scattered).
4. How to reduce it, and why that would help.

Weak: “There was human error.” Strong: “Heat was lost from the polystyrene cup to the surroundings, a systematic error that made the measured temperature rise too small, so the calculated enthalpy change was less exothermic than the true value. Adding a lid and extrapolating the cooling curve back to the time of mixing would reduce this error.”

Mistakes are different

A mistake (sometimes called a “blunder”) isn’t an experimental error in the scientific sense: misreading a scale, recording 21.30 instead of 23.10, using the wrong solution, or spilling some product. The right response to a mistake is to identify it and repeat the measurement, not to average it in or blame “random error”.

A worked example

Four students each measure the enthalpy change of neutralisation of HCl with NaOH (accepted value −57 kJ/mol). Their mean results are −51, −52, −51 and −52 kJ/mol, and each student’s repeats agree to within ±1 kJ/mol.

The results are precise (close together) but not accurate (all about 10% too small in magnitude). That pattern points to a systematic error shared by everyone, most likely heat lost from uninsulated cups. Repeating more times won’t fix it; improving the insulation and correcting for cooling will.

Key takeaways

• Random errors scatter results unpredictably and reduce precision; repeating and averaging reduces them.
• Systematic errors shift all results the same way and reduce accuracy; repeating doesn’t help.
• Detect systematic errors by comparing with accepted values or other methods; reduce them by calibration and better methods.
• Precise results can still be inaccurate if a systematic error is present.
• In evaluations, name the error, classify it, state its effect and suggest a specific fix.