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Systematic and Random Errors


Whenever we measure any physical quantity using an instrument there is always an error associated with it. Such errors are of two kinds – Systematic error and Random error.

Systematic error:

Systematic errors are errors which do not change even if the measurement is carried out many number of times. They are consistent errors, fixed in value and always occur in the same direction.

The most common source of systematic errors are defective instruments. Suppose you have a defective weighing scale whose 0 mark has been shifted to the 1kg mark due to glitches in the device. If you measure the weight of person as 64kg using this defective scale, then we understand that the value obtained is incorrect and that the actual weight of the man is 63kg. This is because the scale has a shifted zero mark and is counting 1kg extra.

These kinds of errors in measuring scales due to shifting of the zero mark are called Zero error.

Notice that in the above example even if you were to repeat your measurement a number of times and consider the average value the error of 1kg would not vanish. This is not the case with random errors as we shall see below.

The only way to remove systematic error is to identify the source of the error and eliminate the problem at the source. For example, if there is a zero error in our instrument we can replace it with a new instrument and measure again to obtain the correct value.                                                                                                                                                     

Random error:

Random errors are errors which cannot be controlled and change with every measurement that we make. The most common source of random errors is human error during measurements. For example, if you measure the length of a pencil a measuring scale you might make a positive error of 1mm. If you were to repeat the measurement once again this time you might make a negative error of 0.5mm.

Notice that these errors are random and do not have a fixed magnitude or direction. Then how do we deal with random errors? Random errors are dealt with the process of averaging. If you repeat a measurement many number of times then the average value is much closer to the true value. The random error gets eliminates on averaging. This is because of the “Law of Errors”.

The law of errors states that the random errors in a measurement follow the normal distribution whose expected value is 0. Hence if we make a large number of measurements the average error tends towards the expected value which is 0.

We summarize the difference between systematic and random errors below.

Differences between Systematic and Random Errors:

  1. Systematic errors are consistent and fixed in direction and magnitude whereas random errors are change in both magnitude and direction.
  2. Random errors can be eliminated by the process of averaging by repeating the measurement many times. On the other hand systematic errors can be removed only by eliminating the cause producing them.
  3. Systematic errors are usually due to faults in the measuring instruments whereas random errors usually occur because of human mistakes during measurements.

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