Random & Systematic Error

Making sense of scatter in repeated measurements

Physics · 1A (alfa) · 23 September 2026
Reading an instrument

The stopwatch has a resolution too

  • A digital stopwatch usually reads to 0.01 s
  • That is its sensitivity — the smallest change it can show
  • Question: is 0.01 s really how precise your reading is?

Two different kinds of error

Random error
Unpredictable, scatters values above and below the true value. Reduced by repeating the measurement and averaging.
Systematic error
Consistent, shifts every reading the same way (e.g. a zero error). Repeating the measurement does not remove it.

Picture it: four dart boards

Describing a set of repeated readings

For a set of repeated measurements:
\text{mean} = \dfrac{\text{sum of readings}}{\text{number of readings}}
\text{range} = \text{highest} - \text{lowest}

Only mean and range today — no median, no mode. They're not part of what Paper 6 asks for, and they'd add clutter on the day we introduce random vs systematic for the first time.

Watch it happen: 6 sample readings

Toy example — not today's real data
2

The swinging apple

Live demonstration

One swing. One event. 28 stopwatches.

  • A model apple on a string will make one complete swing: out and back
  • Before it swings: write down your own prediction of the time, on paper
  • Then everyone times the same single swing, independently, on their laptop
Before we time it

What exactly is "one complete swing"?

One swing lasts 2.5 s here, close to our estimate. Angle exaggerated.

Predict: how much will the 28 readings differ?

  • Less than 0.2 s apart
  • Between 0.2 and 0.5 s apart
  • More than 0.5 s apart
Data collection

Time it now — independently, no comparing

  • Start your stopwatch app now
  • Start at the release, stop when the apple is back at the release point
  • Write your value on the board when called — don't change it after seeing other people's values

28 readings of the same swing

Time / s — type each value as it is read out (comma or point both work)

28 independent readings of one single swing (not 28 separate swings). If left empty, the next slides use example data.
Now the recap

Your predictions vs. the real spread

3

Reading the data

Does any value look strange?

Click a point to mark it yourself.

Discard it, or keep it?

Where does the spread come from?

Is that scatter random or systematic?

?

An open question

Not answered today

How could you make each single reading more precise?

  • Take a moment — what would you personally change?

We'll come back to this on 28 October, with the pendulum lab — physics has an answer you probably haven't thought of.

Exam-style · try it together · 1

Rolling ball

A student times a ball rolling down a ramp five times. Her results are 1.84 s, 1.79 s, 2.31 s, 1.82 s and 1.80 s.

  1. Identify the anomalous result. [1]
  2. Calculate the mean time, ignoring the anomalous result. Give your answer to 3 significant figures. [2]
  3. Suggest one reason why her results are not all the same. [1]
(a) 2.31 s · (b) (1.84 + 1.79 + 1.82 + 1.80) / 4 = 7.25 / 4 = 1.8125 → 1.81 s · (c) her reaction time varies
Exam-style · try it together · 2

The balance that isn't zero

With nothing on it, a digital balance reads 0.3 g. A student places a stone on the balance and it reads 25.6 g.

  1. State the name of this type of error. [1]
  2. Calculate the correct mass of the stone. [1]
  3. The student weighs the stone five times and takes the mean. Explain whether this removes the error. [1]
(a) zero error (a systematic error) · (b) 25.6 − 0.3 = 25.3 g · (c) no: every reading is 0.3 g too high, so the mean is too
Now on your own

Lab 2 worksheet

  • Fill in the stopwatch's sensitivity and your own reading
  • Copy the class data into the grid, cross out the anomaly
  • Calculate mean and range yourself
  • Start exercises 3–6 — finish them at home

In summary

  • A single reading is limited by both the instrument's sensitivity and human reaction time
  • Repeating a measurement and averaging reduces random error — not systematic error
  • An anomalous result needs a reason before it's excluded
  • Open: how do we make a single measurement more precise? — back to this on 28/10