Error Cause and Types

Description:

Precision

It is the degree of exactness or refinement of a measurement. It defines the limitation of measuring instrument. It is not the result of human error or lack of calibration.

Accuracy

It is the extent to which a reported measurement approaches the true value. It depends upon the number of significant figures in it. The larger the significant digits, the higher the accuracy. Problem with accuracy are due to errors. As we reduce the errors, measurements accuracy increases.

Example − Suppose true value of a certain length is 4.567, let it is measured as 4.4 by an instrument of least count 0.1 cm and 3.32 by an instrument of least count 0.01m.

First reading is more accurate (because it is closer to the true value) but less precise (its resolution is only 0.1 cm). Second reading is less accurate but more precise.

Errors

The uncertainty in a measurement is called ‘error’. It is difference between the measured and the true values of a physical quantity.

In general, the error in measurement can be broadly classified as

• Systematic errors
• Random errors
• Least count errors

Systematic errors

Those errors that tend to be in one direction, either positive or negative. These errors are known errors and these can be corrected.

Some of the sources of systematic errors are

• Instrument errors

  It arises from the errors due to imperfect design or calibration of the measuring instrument.

• Imperfect technique

  Imperfection in experimental technique or procedure causes these type of errors.

• Personnel errors

  These errors are the results of human mistakes made while measuring a physical quantity.

Random errors

The random errors are those errors, which occur irregularly and hence are random with respect to sign and size. These errors arise due to random and unpredictable fluctuations in experimental conduction, personal errors by the observer.

These errors are unknown errors, yet they can be corrected by considering the average of - number of measurements of the same quantity.

Least count errors

The smallest value that can be measured by the measuring instrument is called its least count. All the measured values are good only up to this value.

The least count error is the error associated with the resolution of the instrument.

Accuracy of measurement is related to the systematic errors and its precision is related to the random errors, which include least count error.