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ACCURACY AND PRECISION
Every measurement is limited by the reliability of the measuring instrument and the 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.
Physics Class 11 Accuracy and Precision Notes
Table 2.9 Data to illustrate accuracy and precision
| Student | Measurement 1 | Measurement 2 | Measurement 3 | Average mass |
| 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 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 is more precise, as they vary slightly from one another but the average mass is not accurate. The data for student C is both precise and accurate. The resolution for A is 0.01 g and that for Bor 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.
Different types of errors :
1. Constant errors. The errors which affect each observation by the same amount are called constant errors. Such errors are due to the faulty calibration of the scale of the measuring instrument. Such errors can be eliminated by measuring the same physical quantity by a number of different methods, apparatus,es or techniques.
2. Systematic errors. The errors which tend to occur in one direction, either positive or negative, are called systematic errors. We can eliminate such errors once we know the rule which governs them. These errors may be of the following types :
(i) Instrumental errors. These errors occur due to the inbuilt defect of the measuring instrument. For example, wearing off the meter scale at one end, zero error in vernier calipers (zero of the vernier scale may not coincide with the zero of the main scale), etc. This error can be detected by measuring a physical quantity with two different instruments of the same type or by measuring the same physical quantity by two different methods.
(ii) Imperfections in experimental technique. These errors are due to the limitations of the experimental arrangement. For Example, errors due to radiation loss in calorimetric experiments, errors due to buoyancy of air when we weigh a body in the air. Such errors cannot be eliminated altogether but necessary corrections can be applied to them.
(iii) Personal errors. These errors arise due to an individual’s bias, lack of proper setting of apparatus, or individual’s carelessness in taking observations without observing proper precautions, etc. For example, when an observer (by habit) holds his head towards the right while reading a scale, he introduces some error due to parallax. Such errors can be minimized if measurements are repeated by different persons or removing the personal bias as far as possible.
(iv) Errors due to external causes. These errors arise due to changes in external conditions like pressure, temperature, wind, etc. For example, the expansion of a scale due to the increase in temperature. Such errors can be easily detected and necessary corrections may be made accordingly. These errors can also be minimized by controlling the external conditions during the experimentation.
3. Random errors. The errors which occur irregularly and at random, in magnitude and direction, are called random errors. Such errors occur by chance and arise due to slight variations in the attentiveness of the observer while taking the readings or because of slight variations in the experimental conditions. For example, if a person repeats the observation a number of times, he may get different readings every time. Random errors have almost equal chances for both positive and negative errors. Hence the arithmetic mean of a large number of observations can be taken as the true value of the measured quantity.
4. Least count error. This error is due to the limitation imposed by the least count of the measuring instrument. It is an uncertainty associated with the resolution of the measuring instrument. The smallest division on the scale of the measuring instrument is called its least count. For example, a meter scale has a least count of 1 mm, its readings are good only up to this value. The error in its reading will be half of this value i.e., ± 0.5 mm or ± 0.05 cm.
5. Gross errors or mistakes. These errors are due to either carelessness of the person or improper adjustment of the apparatus. No corrections can be applied for gross errors.
For Your Knowledge Physics Class 11 Accuracy and Precision Notes
> Least count errors are random errors but within a limited size; they occur with both random and systematic errors.
> The accuracy of measurement is related to the systematic errors but its precision is related to the random errors, which include the least count error also.
2.31 ABSOLUTE ERROR, RELATIVE ERROR, AND PERCENTAGE ERROR
Elimination of error. The normal or Gaussian law of random errors shows that the probability of occurrence of positive and negative errors is the same, so random error can be minimized by repeating measurements a large number of times. Then the arithmetic mean of all measurements can be taken as the true value of the measured quantity.
If the measured values of a physical quantity, then its true value is given by the arithmetic mean,