Different Types of Errors in Measurement

What is error?

 - Error is defined as difference between the true value and the measured value.

 - True value is the average of the infinite numbers of measurements where measured value is the precise value.

 - Measurement of any quantity is done by comparing it with derived standards and they are not completely accurate.

 - Some errors are constant in nature due to unknown reason, Some are random in nature and some are gross blunder on the part of the experimenter.

Types of Errors

Errors in measurement may happen from various sources which are generally categorized into 3 types.
  1. Random Errors

 2. Gross Errors

 3. Systematic Errors 

1. Random Error

 - Random errors are caused by the sudden change in experimental conditions or noise or tiredness in the working person.

 -  The situation or disturbances which cause these errors are unknown, hence they are termed as random errors.

 - This type of error remain even after removal of the systematic error hence this error also called residual error.

 - This type of errors can be reduced by taking the average of a large number of readings.

2. Gross Error

 - Errors in reading instruments or recording or calculating measurement results are known as gross errors.

 - This type of error is common in measurement as complete elimination is not possible.

 - These error can be prohibited by 

i.  Careful reading and recording of information.
ii. Taking number of readings of the instrument by different operators. 

3. Systematic Error

Systematic errors are classified in 3 categories

A. Observational error

 - These type of error occurs due to wrong observation or reading the instrument.

 - These error occurs mainly while reading the Voltmeter, Ammeter where the pointer resets slightly above the surface of the scale.

 - Highly accurate meters with mirror scale or digital display can eliminate these errors.

B. Environmental Error

 - These types of errors mostly happens due to the temperature, force, moisture, vibrations, electrostatic or magnetic field. 

 - These error can be minimized by 

i.   Placing instrument in temperature-controlled condition.
ii.  Use instrument which is free from environmental effects.
iii. Ensure that there is no external electrostatic or magnetic field.

C. Instrumental error

 - These errors occur due to improper use, loading effect or due to wrong construction of the instrument.

 - These error classified in 3 categories

a. Inherent Limitation of Devices

 - These errors are inbuilt in instruments because of their mechanical arrangement.

 - They may happen due to manufacturing, Operation or calibration.

 - These types of errors will make the mistake to study very low or very high.

 - They can be avoided by selecting appropriate instrument and proper calibration.

b. Abuse of Apparatus

 - The error due to operator fault.

 - Used of instrument in an unintelligent way may give an enormous result.

 - Poor initial adjustment, failure to adjust the zero of instrument etc. are the causes of these error.

c. Effect of Loading

 - These error occur due to the measurement work in the device.

 - When an instrument of lower sensitivity is used with a heavier load the measurement it makes is inaccurate.

Calculation of Errors

These errors are classified in 3 types

1. Absolute error

2. Percentage error

3. Relative error

e.g

A length was calculated to be 10.2 cm but the absolute length was 10.14 cm.then

Absolute error = | Measured value - Exact value |

                        = | 10.2 - 10.14 |

                        = 0.06 cm

Percentage error = (|Measured value - Exact Value| ÷ Exact value) x 100

                           = (0.06 ÷ 10.14) x 100

                           = 0.59%

Relative error = | Measured value - Exact value | ÷ Exact value

                       = 0.06 ÷ 10.14

                       = 0.00591