Introduction
Measurement is essential to our understanding of the outside world, and millions of years of life have developed our sense of measurement. Measurements require tools that scientists quantify. The problem is that every measurement result of every measurement tool contains some uncertainties. This uncertainty is called error. Accuracy and precision are two important factors that must be considered when measuring. Every calculated quantity has accuracy, precision, and errors.
Accuracy
Accuracy of measurement is defined as the extent to which the observed data is close to the true value. It indicates that the lesser the deviation from the true value, the more will be the accuracy of measurement. Only the precise measurement doesn't mean the accurate measurement. Only the precise measurement doesn't mean the accurate measurement. The accuracy of the measurement depends upon the correct setting and correct calibration of the instrument.
The above diagram illustrates the meaning of accuracy more clearly. If the center of the circle is the true value, and black dots are measurements then the first figure has low accuracy because the majority of values obtained are far from true value while the second figure is highly accurate because the majority of values are close to the true value
Example:
The correct length of a rod is measured as 5.234m. One person measured it as 5.2m and B measured it as 5.54 m using the devices they have. Here, the measurement done by A is more accurate than that made by B because the measurement is done by A is closer to the true value.
Summary of Accuracy
- Accuracy refers to the closeness of a measurement to the true value of the physical quantity
- It depends on the correct setting and correct calibration of the instrument.
- The least count is also known as the minimum inaccuracy in the measurement.
Precision
Precision is the degree to which the observed values are least scattered. It means how close the different measurements are. In other words, the precision of measurement is defined as the extent to which the given set of measurements of the same physical quantity is close to the mean value. This means value need not be the true value. Precise measurement need not be accurate.
The above figure illustrates the meaning of precision more clearly. In both measurements, the result of each measurement is very close to each other meaning both the measurements are precise. Precision has nothing to do with the true value of the physical quantity.
Precision is determined by the least count of the measurement. The smaller the least count, the greater is the precision.
Example:
Suppose the length of a stick is measured by Vernier calipers. the set of values recorded by the instrument is 89.1 mm, 89.0 mm, and 89.2 mm. If we take the range, it is found to be 89.2 - 89.0 = 0.2 mm. If we use the ruler having the least count of 1mm, the reading is found to be 89 mm, 88 mm, and 90 mm, the range of measurement is 90 mm - 88 mm = 2 mm. Among these measurements, the measurement done by Vernier calipers is more precise than the measurement done by the ruler. Because the range of measurement is least in the first case.
Summary of Precision
- Precision means how close the given set of measurement is.
- It depends in the least count of the device which is used to measure.
- Smaller the least count, greater is the precision.
Rounding Off (Approximation)
It is necessary to express any measurement up to the correct significant figure. So the measurement should be rounded off to the correct significant figures. Here are the basic rules of approximation:
- If the succeeding digit in a measurement is more than 5 then the digit at the place to be rounded is left as it is.
For example: 2.24 ≈ 2.2 - If the succeeding digit in a measurement is more than 5 then the digit at the place to be rounded off is increased by one.
For example: 2.46 ≈ 2.5 - If the succedding digit in a measurement is 5 then the digit at the place to be rounded off is increased by one if it is odd digit and kept as it if the digit is even.
For example: 2.45 ≈ 2.4
2.75 ≈ 2.8