*“I would rather be roughly correct, than precisely wrong.”*

~ anonymous lazy student during practical lessons

Precision and accuracy, while both desirable, are two different concepts.

Single Measurement

Roughly speaking, precision is related to the **uncertainty** of a measurement. Accuracy**,** on the other hand, is related to the **error** in a measurement.

Take for example two measurements A and B.

True value: 4.77 m

Since A and B have uncertainties of 0.1 m and 0.01 m respectively, B is a more precise measurement.

However, A’s error of 0.03 m is smaller than B’s error of 0.20 m. So A is a more accurate measurement.

Repeated Measurements

If we are talking about a set of repeated measurements, then precision is related to the **spread** among the measured values, whereas accuracy is related to the **deviation** (of the mean value) from the true value.

Take for example data sets A and B shown below.

Since A’s distribution has a smaller spread (about its mean value), it is a more precise data set.

However, B’s mean value is closer to the true value, so B is a more accurate data set.

Experimental Data Plotted on Graph

When the data collected from an experiment is plotted on a graph, precision is related to the **scatter** (about the best-fit-line), whereas accuracy is related to the deviation of the BFL from the theoretical line.

Take for example the results of two experiments A and B shown below (dashed line represents the theoretical line).

Since A’s graph has a smaller scatter about the BFL, A is a more precise experiment.

However, B’s BFL is closer to the theoretical line. So B is a more accurate experiment.

Random and Systematic Errors

In theory, random errors should only affect precision but not accuracy. Inaccuracy can only be caused by systematic errors.

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**Video Explanation **

Precision vs Accuracy (xmphysics)

**Concept Test **

QQ0027

**Interesting**

William Tell and Mars Landing (Ted-Ed)

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