ACCURACY and PRECISION

ACCURACY AND PRECISION

Every measurement is limited by the reliability of the measuring instrument and skill of the person making the measurement. If we repeat a particular measurement, we usually do not get precisely the same result as each result is subject to some experimental error. This imperfection in measurement can be described in two ways:

1. Accuracy. It refers to the closeness of a measurement to the true value of the physical quantity. It indicates the relative freedom from errors. As we reduce the errors, the measurement becomes more accurate.
2. Precision. It refers to the resolution or the limit to which the quantity is measured. Precision is determined by the least count of the measuring instrument. The smaller the least count, greater is the precision. If we repeat a particular measurement of a quantity a number of times, then the precision refers to the closeness of the set of values so obtained.

• We can illustrate the difference between accuracy and precision with the help of an example. Suppose three students are asked to find the mass of a piece of metal whose mass is known to be 0.520 g. They obtain the data given in Table 2.9.

Data to illustrate accuracy and precision:

Student Measurment-1Measurment-2Measurment-3Measurment-4 A 0.52 g 0.51 g 0.50 g 0.51 g B 0.516 g 0.515 g 0.514 g 0.515 g C 0.521 g 0.520 g 0.520 g 0.520 g

The data obtained by the student A are neither very precise nor accurate, the individual values differ widely and also the average value is not accurate. The data for student B are more precise, as they vary slightly from one another but the average mass is not accurate. The data for student C are both precise and accurate. The resolution for A is 0.01 g and that for B or C is 0.001 g

ERRORS IN A MEASUREMENT

Error in a measurement. Every measurement is done with the help of some instrument. While making the measurement, some uncertainty gets introduced in the measurement. As a result, the measured value is always somewhat different from the actual or true value. The error in a measurement is equal to the difference between the true value and the measured value of the quantity.

Error = True value — Measured value

An error gives an indication of the limits within which the true value may lie. Every measurement has an error. Every calculated value which is based on measured values has an error.

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