# Errors in Measurements

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The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is called error. Every calculated quantity which is based on measured values also has an error.

Error = true value – measured value

Types of Errors

Errors may arise from different sources. There are classified as follows :

1. Systematic errors : Errors with known causes and therefore can be minimised. The main sources of systematic errors are as follows:

(i) Instrumental error;
(ii) Personal error;
(iii) Errror due to wrong setting of apparatus in an experiment
(iv) Error due to change in external factors like figure, temperature etc. during an experiment.

2. Random errors : Errors for which the causes are not known precisely and can be minimised by taking multiple measurements.

These errors are due to unknown causes. Therefore they occur irregularly and are variable in magnitude and sign. Since the causes of these errors are not known precisely they can not be eliminated completely. For example, when the same person repeats the same observation in the same conditions, he may get different readings at different times.

Random errors can be reduced by repeating the observation a large number of times and taking the arithmetic mean A.M) of all the observations. This mean value would be very close to the most accurate reading.

Note :- If the number of observations is made n times then the random error reduces to (1/n) times.

Example : If the random error in the arithmetic mean of 100 observations is ‘x’ then the random error in the
arithmetic mean of 500 observations will be x/5.

3. Gross errors: arises due to the carelessness of the observer and hence can be minimised by taking average of all readings.

For example :
(i) Reading instrument without proper initial settings.
(ii) Taking the observations wrongly without taking necessary precautions.
(iii) Exhibiting mistakes in recording the observations.
(iv) Putting improper values of the observations in calculations.

These errors can be minimised by increasing the sincerity and alertness of the observer.

Least count errors : Least count is the smallest value that can be measured by the measuring instrument. The error associated with the resolution of the instrument is called the least count error.