Question Details

Accuracy of measurement is determined by

Options

A

Absolute error

B

Percentage error

C

Both

D

Both

Correct Answer :

Percentage error

Solution :

The correct answer is Percentage error.

To understand why percentage error determines the accuracy of a measurement, let us look at the definitions of the terms involved:
1. Absolute Error: This is the magnitude of the difference between the true value of the quantity and the individual measured value. It is given by:
Absolute Error=|True Value-Measured Value|
Absolute error only tells us the size of the error in the same units as the measurement, but it does not convey how significant the error is relative to the total quantity being measured. For example, an absolute error of 1 cm is extremely large if we are measuring a small object of length 2 cm, but it is negligible if we are measuring the length of a football field (approx. 100 meters).

2. Relative Error and Percentage Error: Relative error is the ratio of the mean absolute error to the mean value of the quantity measured. When expressed as a percentage, it is called the percentage error:
Percentage Error=Absolute ErrorTrue Value×100
Percentage error gives a relative measure of the scale of the error against the actual size of the measurement. Therefore, it directly determines the accuracy of a measurement. A smaller percentage error indicates a higher accuracy of the measurement, regardless of the magnitude of the absolute quantities involved.

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