Error Analysis, Classification, Types and Definition of Errors | Free online notes, study materials on Physics for NEET, JEE, AIPMT, IIT


No measurement is perfect. Measured value of a physical quantity is always different from the true value. The difference between true and measured value of a physical quantity is termed Error. The errors involved in measurement cannot be removed completely.
Two important terms measurement and error are - Accuracy, Precision and Discrepancy
Accuracy: This indicates how close the measured value is to the true value of the quantity. Accuracy increases with reducing errors. This means as we reduce the errors, the measurement becomes more accurate.
Precision: This indicates as to what resolution or limit a quantity has been measured. It is not necessary that a more precise value will also be more accurate.
Discrepancy: The difference between the two measured values of a physical quantity is known as discrepancy.
Other Topics from this Chapter
Dimensions, Dimensional Formulae, Dimensional Equation
Dimensional Analysis and its Applications

Classification of errors can be done in two ways. First, based on the cause of errors such as - Systematic Errors and Random Errors. Second classification is based on the magnitude or size of errors such as - Absolute Error, Mean Absolute Error, Relative or Functional Error, Percentage Error.
Systematic Errors
These are the errors that happen because of various causes which are known to us. A systematic error can, therefore, be minimised. Systematic errors may be due to imperfect technique, alteration of the quantity being measured, carelessness or mistakes on the past of observer. These errors occur in one direction only hence, either positive or negative. If the measured value is greater than the true value, the error is said to be positive and if the measured value is lesser than the true value then it will be said as negative. Systematic errors can be of following types -
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Instrumental Error
These errors arise when the measuring instrument or apparatus itself has some defect in it such as:  improper calibration, defect in designing, zero error (in vernier calipers or screw gauge or meter scale). An instrument error is a constant type of error. These errors can be minimised by using more accurate instruments, applying zero correction, as required.
Observational or Personal Error
Such errors are caused mostly due to carelessness or casual behaviour of an observer. For example, if an observer while reading the volume of water in a beaker becomes casual and keeps his eyes below the meniscus, his reading will be wolf because of Parallax. Also termed as Gross Error, may be due (i) negligence towards sources of error due to overlooking of sources of error by the observer, (ii) the observer, without carrying for last count goes on taking wrong observations, (iii) wrong recording of observation, etc.
Error due to Imperfection and Unavoidable Conditions
As the name suggests these errors are due to the external conditions or due to ignoring certain facts. For example, errors due to changes in temperature, pressure, humidity, air resistance etc. may sometimes affect the final result for not taking these factors into consideration. However, these errors can also be reduced by applying proper corrections to the formula used.
How to minimise Systematic Errors
Systematic errors can be minimised by more accurate instruments, and improved experimental techniques. One should take proper precautions and remain unbiased as far as possible while doing experiments. Further, necessary corrections should be done for the instruments having zero errors after talking readings.
Random Errors
The errors arise due to unknown causes. Random errors would occur irregularly and can have any sign - positive or negative. The magnitude or the size of such errors can also vary randomly.  Since the causes of random errors are not known so, it is not possible to remove them completely.
Least Count Error
The smallest value of the measurement that can be directly taken from a measuring instrument is called the least count (LC) or resolution of the instrument. LC error can arise and depends on the precision provided by the measuring instrument. Thus last count error is another type of constant error and can be reduced by using high precision instruments along with improved experimental techniques. (Please find in our separate post - Formula for How to calculate LC of vernier callipers, screw gauge in Errors in Measurement)
Absolute Error
The magnitude of the difference between the true value and the measured value is called absolute error. It is always positive.
Mean Absolute Error
The arithmetic mean of the magnitudes of individual absolute errors is called the mean absolute error. Thus,
Error Analysis, Classification, Types and Definition of Errors

Relative or Fractional Error
The relative error or fractional error is the ratio of the mean absolute error Damean to the mean value of the quantity measured.
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Percentage Error
The relative error expressed in percentage is Percentage Error. It is denoted by da.
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Standard Error
The errors which take into account all the factors affecting the accuracy of result, is known as the Standard Error.
Probable Error
The errors calculated by using the principle of probability, are Probable Errors. According to Bessels Formula,

 Combination of Errors, Errors in Measurement >>

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