Errors in Measurement and Classification of Errors

True Value:

It is not possible to determine the true of quantity by experiment means. True value may be defined as the average value of an infinite number of measured values when average deviation due to various contributing factor will approach to zero.

Measured Value:

It may be defined as the approximated value of true value. It can be found out by taking means of several measured readings during an experiment, by applying suitable approximations on physical conditions. Now we are in a position to define static error. Static error is defined as the difference of the measured value and the true value of the quantity. Mathematically we can write an expression of error as, dA = A_m - A_t where, dA is the static error A_m is measured value and A_t is true value. It may be noted that the absolute value of error cannot be determined as due to the fact that the true value of quantity cannot be determined accurately. Let us consider few terms related to errors.

Types of Errors:

Basically there are three types of errors on the basis; they may arise from the source.

Gross Errors:

This category of errors includes all the human mistakes while reading, recording and the readings. Mistakes in calculating the errors also come under this category. For example while taking the reading from the meter of the instrument he may read 21 as 31. All these types of error are come under this category. Gross errors can be avoided by using two suitable measures and they are written below:

1.      A proper care should be taken in reading, recording the data. Also calculation of error should be done accurately.

2.      By increasing the number of experimenters we can reduce the gross errors. If each experimenter takes different reading at different points, then by taking average of more readings we can reduce the gross errors.

Systematic Errors:

In order to understand these kinds of errors, let us categorize the systematic errors as

Instrumental Errors:

These errors may be due to wrong construction, calibration of the measuring instruments. These types of error may be arises due to friction or may be due to hysteresis. These types of errors also include the loading effect and misuse of the instruments. Misuse of the instruments results in the failure to the adjust the zero of instruments. In order to minimize the gross errors in measurement various correction factors must be applied and in extreme condition instrument must be re-calibrated carefully.

Environmental Errors:

This type of error arises due to conditions external to instrument. External condition includes temperature, pressure, humidity or it may include external magnetic field. Following are the steps that one must follow in order to minimize the environmental errors:

·         Try to maintain the temperature and humidity of the laboratory constant by making some arrangements.

·         Ensure that there should not be any external magnetic or electrostatic field around the instrument.

Observational Errors:

As the name suggests these types of errors are due wrong observations. The wrong observations may be due to PARALLAX. In order to minimize the PARALLAX error highly accurate meters are required, provided with mirrored scales.

Random Errors:

After calculating all systematic errors, it is found that there are still some errors in measurement are left. These errors are known as random errors. Some of the reasons of the appearance of these errors are known but still some reasons are unknown. Hence we cannot fully eliminate these kinds of error.