Accuracy Precision Error Measurement

The accuracy of a measurement refers to how near it is to the proper value for that measurement. The precision of a measurement system refers to the degree to which repeated measurements coincide (Which are repeated under the same conditions). Measurements can be both exact and accurate, precise but not accurate, precise but not accurate, or neither.

Low precision, high accuracy the hits on this bullseye are all in the centers, but none are close to each other; this is an example of precision without accuracy.

Accuracy and Precision

The accuracy of a measurement is determined by its “nearness” or proximity to the true value or actual value (am)of the quantity. Let a1,a2,a3,a4…..an, be a quantity ‘a’with ‘n’ measured values. After that, the true value is defined as follows:

 am=a1+a2+a3+a4…+an/n

Assume your height is 183 cm. When measured with an equipment (measuring tape and a clever laser beam), it measures 182.9995 cm. A second measurement (with a meter rod and a 6th grader) results in 195 cm.  As you can see, the initial measurement produced a result that is closer to your real (true) height. The first measurement, as a result, is more precise than the second.

Assume that our sixth-grader enjoys measuring heights. He measures your height three more times and comes up with the following numbers: 197 cm,195.3 cm, and 196.1 cm. Are you sure these figures are correct? Of course not; they are grossly underestimating your height. However, we can observe that all of these measurements are close to each other, i.e. 197 cm,195.3 cm,196.1 cm, and 195 cm.  They are extremely accurate measurements.

As a result, accuracy refers to how closely the multiple measured values are related to one another. On the other hand, accuracy refers to how close the measured values are to the true value of the quantity.

Errors in Measurement

If a measurement is both accurate and precise, it can be trusted. The measurement error, am of the quantity, is the difference between the measured and real values. The measurement error, the less precise the measurement.

The measurement error is the uncertainty in a measurement’s value. This is the range of variation between the measurement and the original value. The error in measuring a quantity ‘a’ is signified by the letter ∆a, which is indicated by placing a delta sign before the quantity’s symbol.

Types of Errors

There are different types of errors like:

Systematic errors

In such errors, the measurement deviates from the true value by a predetermined amount. As a result, these mistakes are predictable. An inaccurate instrument, changes in the physical conditions at the time of measurement, human error, and other factors are the most common causes of systematic errors.

Random errors

Unknown sources are to fault for these mistakes. These kinds of errors can be eliminated by taking a large number of readings and calculating the mean.

Relative errors

The relative error is calculated as the ratio of the mean absolute error to the true value of the quantity.

Relative error=(Mean absolute error)/am

In the above case, Relative error=12.85183=0.07022cm

Percentage Errors

The percentage mistake is calculated by converting the relative error to a percentage, i.e. Percentage error = Relative error×100%

Percentage error = 0.07022cm×100%=7.022% in the example above.

Errors in addition and Subtraction

Leta±∆aand(b±∆b) be two quantities.

Suppose X=(a±∆a)±(b±∆b)

Then error in X i.e., ∆X=±(∆a+∆b)

As a result, whether adding or subtracting, errors occur.

Instrumental errors

Instrumental errors are errors that occur as a result of an instrument’s lack of precision. Instrumental Error can be caused by a number of factors:

1. The instrument will not be used if it is not well-designed and accurate.
2. The calibration of the instrument is inaccurate.
3. If the margins of the scale have been worn away or the scale has been cracked in any manner,
4. When an instrument provides a false reading rather than the correct one.

Conclusion

The accuracy of a measurement refers to how near it comes to the right value for that measurement. The precision of a measurement system refers to the degree to which repeated measurements agree (Which are repeated under the same conditions).

High precision, low precision This bullseye has hits that are close together but not close to the middle; this is an example of precision without accuracy.

A measurement can be believed if it is both accurate and precise. The discrepancy between the measured and true values is the measurement error, am of the quantity. The measurement becomes less exact as the measurement error increases.

The measurement deviates from the true value by a predefined amount in such situations. As a result, certain errors are expected. The most typical sources of systematic mistakes are an incorrect instrument, changes in the physical conditions at the time of measurement, human error, and other factors.