Random and systematic errors in physical measurements or physics experiments | Precision and accuracy & Uncertainty

Here we will briefly define and explain the common terms related to Random errors and systematic errors in physical measurements (also in Physics experiments). We will talk about terms like Precision and accuracy & Uncertainty.

Define Random errors

These are errors that are due to the experimenter. The size of these errors depends on how well the experimenter can use the apparatus. The better experimenter you are the smaller these errors will be. The way to reduce these errors, apart from simply being careful, is to repeat the readings and take an average.

Define Systematic errors

These are errors that are due to the apparatus. They can result from faulty apparatus, badly calibrated apparatus, or a zero error. The only way to eliminate systematic errors is to re-calibrate the apparatus or change it!

Precision and accuracy

Figure 1 shows the difference between precision and accuracy. The closer the grouping the higher the precision. A more symmetrical grouping about the center shows a higher degree of accuracy.

figure 1: Precision and accuracy

Measurements can also be considered in terms of their repeatability (whether they can be repeated), their reproducibility (whether their values can be reproduced when measured many times), and their resolution (an example of resolution would be pixels per mm^2 in an image).


The uncertainty (ΔQ) in a quantity Q (Q = a + b) is:
ΔQ = Δa + Δb
where Δa and Δb are the uncertainties in the quantities a and b.

The percentage uncertainty (%Q = (ΔQ/Q) × 100) is:
%Q = %a + %b

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