Accuracy and Precision - Physics For Class 11/NEET/JEE

Science is based on observation, experiment, measurement and calculation. In order to measure the physical quantities involved in the experiments, we need some instruments. However, quite often, it is found that the instruments which are used to measure the physical quantities don’t give the accurate measurements.

But, what is accuracy ? Do we need an instrument which records accurate measurements or we need an instrument which records precise measurements ? What is the difference between accuracy and precision ? Let’s understand it with the help of a suitable example.

Example:

There are two thermometers A and B.

The temperature inside a refrigerator was measured five times by using both the thermometers simultaneously.

The readings recorded by thermometer A are: 12.1^oF, 13.5^oF, 15.4^oF, 14.5^oF, 16.0^oF

The readings recorded by thermometer B are: 18.1^oF, 18.2^oF, 18.1^oF, 18.2^oF, 18.1^oF

If the actual temperature inside the refrigerator was 15^oF, then which thermometer is more accurate and which one is more precise ?

LET US DETERMINE

On taking the average of the readings recorded by A, we get:

Average reading = (12.1 + 13.5 + 15.4 + 14.5 + 16.0) / 5 = 14.3^oF

On taking the average of the readings recorded by B, we get:

Average reading = (18.1 + 18.2 + 18.1 + 18.2 + 18.1) / 5 = 18.14^oF

 

 Test of Accuracy

The average reading of A is 14.3^oF and it close to the actual value which is 15.0^oF. Thus, the temperature recorded by thermometer A is more accurate.

The average reading of B is 18.14^oF and it is far from the actual value. Thus, the temperature recorded by thermometer B is less accurate.

 

Test of Precision

The lowest reading by A was 12.1^oF and the highest reading was 16.0^oF.

Difference between the highest and the lowest reading = 16.0^oF  – 12.1^oF  = 3.9^oF  

This difference is called Range.

 

The lowest reading by B was 18.1^oF and the highest reading was 18.2^oF.  

Range = 18.2^oF – 18.1^oF  = 0.1^oF  

 

The readings recorded by B have a short range, i.e. the readings are close to each other (though they are far from the actual value). In other words, the measurements are consistent and they are NOT SCATTERED much. Thus, we say that the measurements obtained by using B are more precise.

The readings recorded by A have a long range, i.e. the readings are not close to each other (though they are close to the actual value). In other words, the measurements are not consistent and they are SCATTERED MUCH. Thus, we say that the measurements obtained by using A are less precise.

 

In fact, for scientific purpose, we need an instrument which gives precise measurement.

 

PROBLEMS FOR PRACTICE

Question 1

In each of the following, determine which set of data is more precise.

(i) Sample A: 32.56,  32.55,  32.48,  32.49,  32.48.

     Sample B: 15.38,  15.37,  15.36,  15.33,  15.32.

 

(ii) Sample A: 8.34,  8.76,  8.55,  8.43,  8.72,  8.65

      Sample B: 9.41,  9.46,  9.39,  9.40,  9.92,  9.19

 

Question 2

In each of the following, determine which set of data is more accurate.

(1) Sample A: 21.3,  22.9,  21.5,  22.4,  23.6.

      Sample B: 25.2,  19.4,  20.7,  20.5,  19.8.

      Actual value = 21.1 

 

(1) Sample A: 85.4,  82.7,  84.1,  83.5,  81.4

      Sample B: 70.1,  77.4 ,  89.8,  94.5,  82.6

      Actual value = 82.5