Q. With suitable example differentiate between accuracy and precision.
Sol. Accuracy : Accuracy is the closeness with which instrument reading approaches the true value of the particular quantity to be measured, that is, accuracy of a measurement means conformity to truth. The accuracy of an instrument is measured in terms of its errors. The most important characteristic of an instrument or measurement system is its accuracy. It is generally expressed as a percentage of either true value or full scale value.
Mathematically, accuracy on the basis of true value, Vt is given by:
Accuracy =
Accuracy =
Where Vmax and Vmin are the maximum or minimum final reading or results obtained after applying all the known corrections to all the various indicated readings and Vt is the true (actual) magnitude of input.
Accuracy of a measurement means conformity to truth.
Precision: Precision refers to the degree of agreement within a group of various measurement or readings of the same parameter of variable.
As seen above, accuracy and precision have totally distinct meanings. Let us illustrate this using following examples:
1. Consider an instrumentation system where the temperature of boiling water at 100?c is being measured using a thermometer. Suppose that four reading are taken using the same thermometer and they are : 100.4?c, 100.3?c, 100.5?c and 100.3?c
2. Consider the case of two voltmeter 'A' and 'B' measuring the voltage at the same point with respect to ground. Assure that the true value of voltage is 50 V while the two voltmeters indicate the values as shown below when four consecutive reading are taken.
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No. or Readings
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Voltmeter 'A'
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Voltmeter 'B'
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Voltmeter 'C'
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1. 50V 48.5V 50.1V
2. 50.2 48.5V 50.1V
3. 48.8V 48.5V 50.80V
4. 50.1V 48.52V 50.1V
It is clear from above that voltmeter 'A' reads very close to the true value of 50 V. However, there is an agreement between the four readings.
On the other hand, voltmeter 'B's' reading are not very close to true value of 50 V. But all the values are very close to each other or same. We can conclude from above that voltmeter 'A' is fairly accurate but not precise while voltmeter 'B' is not accurate and precise.
If we consider of third voltmeter 'C' which reads 50.1, 50.1, 50.80, 50.1 for the same true value of 50 V, then we can say that voltmeter C is both accurate and precies.
Sensitivity : The sensitivity of the instrument is the ratio of the change in output (response) of the instrument to the change of input or measured variable.
It denotes the smallest change in the value of a measured variable to which instrument responds. Sensitivity is an important property of the instrument which is determined by design. The numerical value of the sensitivity is influenced by the requirement of instrument application. The choice will be decide by the smallest subdivision desired by the conditions of the test treatment.
Sensitivity and responsiveness are frequently confused, as in speaking of thermometer which is sensitive to 0.1 °c. In accordance with the definition of the two terms, it is correct to say that the thermometer will respond to a change in ± 0.1°c.