Errors in Measurement
The uncertainty in a measurement is called an error. Random error, systematic error and gross error are the three possible errors.
i) Systematic errors Systematic errors are reproducible inaccuracies that are consistently in the same direction. These occur often due to a problem that persists throughout the experiment. Systematic errors can be classified as follows
1) Instrumental errors When an instrument is not calibrated properly at the time of manufacture, instrumental errors may arise. If a measurement is made with a meter scale whose end is worn out, the result obtained will have errors. These errors can be corrected by choosing the instrument carefully.
2) Imperfections in experimental technique or procedure These errors arise due to the limitations in the experimental arrangement. As an example, while performing experiments with a calorimeter, if there is no proper insulation, there will be radiation losses. This results in errors and to overcome these, necessary correction has to be applied.
3) Personal errors These errors are due to individuals performing the experiment, may be due to incorrect initial setting up of the experiment or carelessness of the individual making the observation due to improper precautions.
4) Errors due to external causes The change in the external conditions during an experiment can cause error in measurement. For example, changes in temperature, humidity, or pressure during measurements may affect the result of the measurement.
5) Least count error Least count is the smallest value that can be measured by the measuring instrument, and the error due to this measurement is least count error. The instrument’s resolution hence is the cause of this error. Least count error can be reduced by using a high precision instrument for the measurement.
ii) Random errors
Random errors may arise due to random and unpredictable variations in experimental conditions like pressure, temperature, voltage supply etc. Errors may also be due to personal errors by the observer who performs the experiment. Random errors are sometimes called “chance error”. When different readings are obtained by a person every time he repeats the experiment, personal error occurs. For example, consider the case of the thickness of a wire measured using a screw gauge. The readings taken may be different for different trials. In this case, a large number of measurements are made and then the arithmetic mean is taken.
If n number of trial readings are taken in an experiment, and the readings are a1, a2, a3,…………………. an. The arithmetic mean is \(\begin{aligned} \text{am} & = \frac{a_{\text{}1} + a_{\text{}2} + a_{\text{}3} + \ldots + a_{\text{}n}}{n} \end{aligned}\) or
\(\begin{aligned} \text{am} & = \frac{1}{n} \sum_{i=1}^{n} a_{\text{}i} \end{aligned}\) (1.2)
Usually this arithmetic mean is taken as the best possible true value of the quantity.
Table 1.8 Minimizing Experimental Error
| Type of error | Example | How to minimize it |
|---|---|---|
| Random error | Suppose you measure the mass of a ring three times using th balance and get slightly diff values. 15.46 g, 15.42 g, 15 | Take more data. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations. |
| Systematic error | Suppose the cloth tape mea that you use to measure the of an object has been stretch from years of use. (As a resu the length measurements ar correct). | Systematic errors are difficult to detect and cannot be analysed statistically, because all of the data is in the same direction. (Either too high or too low) |
Certain procedures to be followed to minimize experimental errors, along with examples are shown in Table 1.8.
iii) Gross Error
The error caused due to the shear carelessness of an observer is called gross error. For example
(i) Reading an instrument without setting it properly.
(ii) Taking observations in a wrong manner without bothering about the sources of errors and the precautions.
(iii) Recording wrong observations.
(iv) Using wrong values of the observations in calculations.
These errors can be minimized only when an observer is careful and mentally alert.