# 1.2.3 Precision and Accuracy

“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. $\displaystyle \begin{array}{l}A:4.8\pm 0.1\text{ m}\\B:4.57\pm 0.01\text{ m}\end{array}$

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.

Video Explanation

Precision vs Accuracy

Concept Test

QQ0027

Interesting

William Tell and Mars Landing (Ted-Ed)