A random limitation scatters repeat readings in no fixed direction. A systematic limitation moves all readings the same way, for example every reading too high.
To answer a question on either, point to the pattern in the supplied evidence and name a physical cause and a fix. This is part of physics investigations and explanations.
How do you read the evidence?
- Look for repeats of the same measurement. If the values differ with no fixed direction, that is scatter, so random.
- Look for a constant offset: every value too high or too low, or a graph line that should pass through the origin but does not.
- Name a cause that fits the pattern (reaction time, instrument zero, parallax, heat lost to the surroundings).
- Give the matching improvement: repeat and average for random scatter; check the zero or use a different method for a systematic shift.
Worked example
Part A: random scatter. Invented data. A student times 20 swings of a pendulum five times: 32.6 s, 33.4 s, 32.1 s, 33.0 s and 32.9 s.
Sum = 32.6 + 33.4 + 32.1 + 33.0 + 32.9 = 164.0 s. Mean = 164.0 ÷ 5 = 32.8 s. The period is 32.8 ÷ 20 = 1.64 s.
The readings scatter between 32.1 s and 33.4 s, a range of 1.3 s, and some are above and some below the mean. This points to random limitation, most likely reaction time when starting and stopping the stopwatch. Timing 20 swings spreads this error over many swings, and repeating and averaging reduces it further.
Part B: systematic shift. Invented data. With the ammeter disconnected, it reads 0.04 A. The voltmeter readings and ammeter readings for a resistor are:
| V / V | 1.0 | 2.0 | 3.0 | 4.0 |
|---|---|---|---|---|
| Measured I / A | 0.14 | 0.24 | 0.34 | 0.44 |
Every current reading is 0.04 A too high, so this is a systematic limitation (zero error). A graph of V against I does not pass through the origin: it meets the I-axis at 0.04 A.
The gradient is still correct, because both points are shifted equally: (4.0 − 1.0) V ÷ (0.44 − 0.14) A = 3.0 ÷ 0.30 = 10 Ω. The true current values are 0.10, 0.20, 0.30 and 0.40 A, giving 10 Ω each time.
The mistake to watch for
A student divides the first pair of readings and reports R = 1.0 ÷ 0.14 = 7.1 Ω, then says “the error is random, so I should repeat and average.”
Mistaken answer: R = 7.1 Ω; random error.
Repeating gives 0.14 A again, because the shift is the same every time. Averaging does not remove it.
The correction is to spot the pattern (all readings 0.04 A too high) and respond with a zero correction: subtract 0.04 A from each reading, or use the gradient between two points. Then R = 10 Ω.
Check yourself
1. A stopwatch shows 0.30 s before it is started. Is this random or systematic, and what should the student do?
Show answer
It is a systematic (zero) error because every reading is shifted by the same amount. The student should subtract 0.30 s from each time, or use a stopwatch that resets to zero.
2. Five repeat readings of a length are 12.3, 12.5, 12.4, 12.6 and 12.2 cm. Is the limitation random or systematic? Give the mean.
Show answer
The values vary both ways around the middle, so the limitation is random. Sum = 12.3 + 12.5 + 12.4 + 12.6 + 12.2 = 62.0, and the mean = 62.0 ÷ 5 = 12.4 cm.
3. A student says, “I repeated the zero-error measurements three times and averaged them, so the systematic error is gone.” Explain why this is not correct.
Show answer
A systematic error affects every repeat the same way, so the average has the same shift. The error is removed only by correcting the zero or using a better instrument or method.
Where this leads next
With limitations identified, the final skill is writing them up in a concise claim-evidence-reasoning answer. The bounds and rounding explainer and the reasoning board help you practise the careful wording. Go back to interpreting the gradient if the zero-error example felt unfamiliar.
Linking error types to the data in front of you is a skill that improves quickly with feedback, which is what online one-to-one Physics tuition provides.