1.8 Errors in measurement

Faulty measurements of physical quantity can lead to errors.

The errors are broadly divided into the following two categories :

a) Systematic errors :

Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy (involving either the observation or measurement process) inherent to the system.

Sources of systematic error may be due to imperfect calibration of the instrument, and sometimes imperfect method of observation.

Each of these errors tends to be in one direction, either positive or negative.

The sources of systematic errors are as follows:

(i) Instrumental error:

This type of error arises due to defective calibration of an instrument,

for example an incorrect zeroing of an instrument will lead to such kind of error ('zero' of a thermometer not graduated at proper place, the pointer of weighting balance in the laboratory already indicating some value instead of showing zero when no load is kept on it, an ammeter showing a current of 0.5 amp even when not connected in circuit, etc).

(ii) Error due to imperfection in experimental technique:

This is an error due to defective setting of an instrument.

For example the measured volume of a liquid in a graduated tube will be inaccurate if the tube is not held vertical.

(iii) Personal error:

Such errors are introduced due to fault of the observer. Bias of the observer, carelessness in taking observations etc. could result in such errors.

For example, while measuring the length of an object with a ruler, it is necessary to look at the ruler from directly above.

If the observer looks at it from an angle, the measured length will be wrong due to parallax.

Systematic errors can be minimized by using correct instrument, following proper experimental procedure and removing personal error.

b) Random errors:

These are the errors which are introduced even after following all the procedures to minimize systematic errors.

These type of errors may be positive or negative.

These errors can not be eliminated completely but we can minimize them by repeated observations and then taking their mean (average).

Random errors occur due to variation in conditions in which experiment is performed.

For example, the temperature may change during the course of an experiment, pressure of any gas used in the experiment may change, or the voltage of the power supply may change randomly, etc