# 1.2 Errors in measurement

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We can only approximate true value with greater accuracy and precision.

Measurement is the basis of scientific study. All measurements are, however, approximate values (not true values) within the limitation of measuring device, measuring environment, process of measurement and human error. We seek to minimize uncertainty and hence error to the extent possible.

Further, there is important aspect of reporting measurement. It should be consistent, systematic and revealing in the context of accuracy and precision. We must understand that an error in basic quantities propagate through mathematical formula leading to compounding of errors and misrepresentation of quantities.

Errors are broadly classified in two categories :

• Systematic error
• Random error

A systematic error impacts “accuracy” of the measurement. Accuracy means how close is the measurement with respect to “true” value. A “true” value of a quantity is a measurement, when errors on all accounts are minimized. We should distinguish “accuracy” of measurement with “precision” of measurement, which is related to the ability of an instrument to measure values with greater details (divisions).

The measurement of a weight on a scale with marking in kg is 79 kg, whereas measurement of the same weight on a different scale having further divisions in hectogram is 79.3 kg. The later weighing scale is more precise. The precision of measurement of an instrument, therefore, is a function of the ability of an instrument to read smaller divisions of a quantity.

In the nutshell,

• True value of a quantity is an “unknown”. We can not know the true value of a quantity, even if we have measured it by chance as we do not know the exact value of error in measurement. We can only approximate true value with greater accuracy and precision.
• An accepted “true” measurement of a quantity is a measurement, when errors on all accounts are minimized.
• “Accuracy” means how close is the measurement with respect to “true” measurement. It is associated with systematic error.
• “Precision” of measurement is related to the ability of an instrument to measure values in greater details. It is associated with random error.

## Systematic error

A systematic error results due to faulty measurement practices. The error of this category is characterized by deviation in one direction from the true value. What it means that the error is introduced, which is either less than or greater than the true value. Systematic error impacts the accuracy of measurement – not the precision of the measurement.

Systematic error results from :

• faulty instrument
• faulty measuring process and
• personal bias

Clearly, this type of error can not be minimized or reduced by repeated measurements. A faulty machine, for example, will not improve accuracy of measurement by repeating measurements.

## Instrument error

A zero error, for example, is an instrument error, which is introduced in the measurement consistently in one direction. A zero error results when the zero mark of the scale does not match with pointer. We can realize this with the weighing instrument we use at our home. Often, the pointer is off the zero mark of the scale. Moreover, the scale may in itself be not uniformly marked or may not be properly calibrated. In vernier calipers, the nine divisions of main scale should be exactly equal to ten divisions of vernier scale. In a nutshell, we can say that the instrument error occurs due to faulty design of the instrument. We can minimize this error by replacing the instrument or by making a change in the design of the instrument.

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