Accuracy and precision- source: mathsis fun.com

## Accuracy and precision-

### Accuracy-

Accuracy means the closeness of an experimental value or the mean value of a set of measurements to the true value. It is a measure of the difference between the mean value & true value. Accuracy expresses the correctness of measurement.

Accuracy = mean value – true value

“Smaller is the difference between mean & true value, greater is the accuracy.”

### Precision –

Precision means how closely two or more measurements of the same quantity agree with one another. It is expressed as the difference between measured value & mean value. Precision gives the extent of agreement of the measured values among themselves.

Precision = measured value –  mean value

“Smaller is the difference between the measured value of repeated measurements of the same quantity, greater is the precision.”

### ” An accurate measurement is always precise, but a precise measurement need not be accurate.”

Example-

measurement 1, measurement 2, average

Student ‘X’-       1.95 g                    1.93 g                          1.94 g

Student ‘Y’ –       1.94 g                   2.05 g                         1.995 g

Student ‘Z’-       2.01 g                    1.99 g                        2.00 g

If the true value for the result is 2.00 g,

student ‘X’ takes two measurements & report the results as these are 1.95 g & 1.93 g. These values are precise because these are close to each other but are not accurate ( because not close to the true value)

student ‘Y’ takes two measurements & report the results as these are 1.94 g & 2.05 g. These values are neither precise nor accurate because these are not close to each other & true value.

student ‘Z’ takes two measurements & report the results as these are 2.01 g & 1.99 g. These values are both precise & accurate because these are close to each other & also close to the true value.