18 min read

Recap G — Accuracy and Precision

Reading target diagrams, accuracy and precision in measurements, and systematic and random errors — 12 worked examples, each with a diagram.

The Big Idea

Imagine throwing darts at a target several times: Accuracy — how close your darts are to the bullseye (the correct value). Precision — how close your darts are to each other (how tight the group is). They are different! You can be precise without being accurate, and accurate on average without being precise.

Four targets showing each combination of high or low accuracy and high or low precision. — $The four combinations.$

1. Reading Targets

A target: tight group on the bullseye. — $Example 1$

Example 1 — tight group on the bullseye

Question: All the shots are close together and on the bullseye. Describe the accuracy and precision. Answer: Close together \to high precision. On the bullseye \to high accuracy. High accuracy, high precision.

A target: tight group away from the centre. — $Example 2$

Example 1 — tight group away from the centre

Question: All the shots are in one tight group, but away from the bullseye. Describe the accuracy and precision. Answer: Close together \to high precision. The group is not on the bullseye \to low accuracy. Low accuracy, high precision.

A target: spread out around the centre. — $Example 3$

Example 1 — spread out around the centre

Question: The shots are spread out, but evenly around the bullseye. Describe the accuracy and precision. Answer: Not close together \to low precision. The middle of the group is the bullseye \to high accuracy. High accuracy, low precision.

A target: spread out and off-centre. — $Example 4$

Example 1 — spread out and off-centre

Question: The shots are spread out and the group is away from the bullseye. Describe the accuracy and precision. Answer: Not close together \to low precision. Not centred \to low accuracy. Low accuracy, low precision.

A target: another tight group. — $Example 5$

Example 1 — another tight group

Question: Another target: a tight group in the outer ring. Describe the accuracy and precision. Answer: Tight \to high precision; outer ring \to low accuracy. Low accuracy, high precision. (The position of the group does not matter — only that it is not the centre.)

Example 1 — another spread

Question: Another target: shots in different rings all around the centre. Describe the accuracy and precision. Answer: Spread \to low precision; centred \to high accuracy. High accuracy, low precision.

2. Accuracy and Precision in Measurements

Dot plot: Weighing a 2 kg bag three times. — $Example 7$

Example 1 — weighing a 2 kg bag three times

Question: A 2 kg bag is weighed three times: 2.51, 2.50, 2.51 kg. Describe the scale. Answer: The readings are very close together \to precise . They are all about 0.5 kg too heavy \to not accurate . This is a systematic error — the scale probably needs to be set to zero.

Dot plot: Measuring a 1.00 m length four times. — $Example 8$

Example 1 — measuring a 1.00 m length four times

Question: A 1.00 m length is measured four times: 0.97, 1.03, 0.99, 1.01 m . Describe the measurements. Answer: The average is \frac{0.97 + 1.03 + 0.99 + 1.01}{4} = 1.00 m — the true value \to accurate . But the readings are spread out \to not very precise (random error).

Dot plot: Measuring a 25 °C room three times. — $Example 9$

Example 1 — measuring a 25 °c room three times

Question: A thermometer in a 25 °C room reads 25.0, 25.1, 25.0 °C. Describe it. Answer: Close together and close to the true value \to accurate and precise .

Dot plot: Timing a 60 s event four times. — $Example 10$

Example 1 — timing a 60 s event four times

Question: A 60 s event is timed as 42, 58, 39, 47 s. Describe the timings. Answer: Spread out \to not precise . Average = 186 \div 4 = 46.5 s, far from 60 s \to not accurate .

Example 2 — a clock that is fast

Question: A clock is always exactly 5 minutes fast. Is it accurate? Is it precise? Answer: It is not accurate — it is always wrong by 5 minutes. It is precise — it is wrong by exactly the same amount every time. This is a systematic error.

Example 3 — improving results

Question: How can you improve (a) precision and (b) accuracy? Answer: (a) Precision: take careful, repeated readings and use a more precise instrument — this reduces random errors. (b) Accuracy: calibrate the instrument (for example zero the scale) and check it against a known standard — this removes systematic errors.

Your turn — try these on paper, then check the answers below. 1 . Shots are tightly grouped on the bullseye. Describe them. 2 . Darts land in all the rings, evenly around the bullseye. Describe them. 3 . What kind of error makes results spread out?

Example 1 — Answers to Your Turn

1 . High accuracy, high precision 2 . High accuracy, low precision 3 . Random errors

You have finished the recap. Now go to the Practice Paper .

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