Precision and Accuracy

Question: Explain ‘the difference between Precision and accuracy with the help of examples?

Precision and Accuracy:

A precise measurement is the one, which has less absolute uncertainty, and an accurate measurement is the one, which has less fractional, or percentage uncertainty or error.

Explanation:

The precision of a measurement is determined by the instrument or device being used and the accuracy of a measurement depends on the fractional or percentage uncertainty in that measurement.

For example:
Case I:
When the length of an object is recorded as 25.5 cm by using a meter rod having smallest division in millimeter, it is the difference of two readings of the initial and final positions. The uncertainty in the single reading as discussed before is taken as ± 0.05 cm which is now doubled and is called absolute uncertainty equal to ± 0.1 cm. Absolute uncertainty, in fact, is equal to the least count of the measuring instrument.
Precision or absolute uncertainty (least count) = ± 0.1 cm
Fractional uncertainty =    (Least count)/(Recorded length)

Fractional uncertainty =      0.1cm /25.5cm           = 0.004

Percentage uncertainty =   0.1cm /25.5cm  x 100  = 0.4%

Case ii:
Another measurement taken by vernier callipers with least count as 0.01cm is recorded as 0.45 cm, It has

Precision or absolute uncertainty (least count) ± 0.01 cm
Fractional uncertainty =   Least Count/Recorded Length

Fractional uncertainty =      0.01 cm/0.45 cm          =            0.02

Percentage uncertainty =  0.01 cm/0.45 cm x 100 = 2.0%

Thus, the reading 25.5 cm taken by meter rule is although less precise but accurate having less percentage uncertainty or error.

Whereas the reading 0.45 cm taken by vernier calipers is, more precise but is less accurate. In fact, it is the relative measurement, which is important
Note:
The smaller a physical quantity, the more precise instrument should be used. Here the measurement 0.45 cm demands that a more precise instrument such as micrometer screw gauge with least count 0.001 cm should have been used

Hence we can Conclude:

A precise measurement is the one which has less absolute uncertainty and an accurate measurement is the one which has less fractional or percentage uncertainty or error.