# Errors In Measurement

Contents

To measure any physical quantity, we compare it with a standard unit of that quantity. No measurement is perfect as the error involved in the process, can not be removed completely. So the difference in the true value and the measured value of a quantity is called error of measurement.

Error = True Value – Measured Value

In general, the error can be further classified as

1. Systematic Errors

2. Random Errors

## 1. Systematic Errors

Those errors that tends to be in one direction, either positive or negative are called systematic errors. Some of the source of systematic errors are as

(I) Instrumental Error

(II) Imperfection in experimental technique or procedure

(III) Personal errors

(IV) Errors due to external causes

## 2. Random Errors

The errors which occur irregularly and at random in magnitude and direction are called random errors. They may also arise due to random and unpredictable variations in experimental conditions like temperature, pressure, voltage supply, vibrations etc. They are also known as chance errors.

Example:- When the person repeats the observations, he may get different readings every time.

Some other errors are as follows

### Least Count Error

The smallest value that can be measured by a measuring instrument is called the list count of the instrument.

This error is occurred due to the limitation imposed by the list count of the measuring instrument.

Example:- A meter scale has a least count of 1 mm, its reading are good only upto this value. The error in its reading will be half of this value i.e ±0.5 mm or ±0.05 cm.

Hence, least count error is the error, associated with the resolution of the instrument.

### Absolute Errors

The magnitude of the difference between the true value of the quantity measured and the individual measured value is called absolute error.

If we take Arithmetic Mean as the true value, then the absolute Errors in the individual measured values will be

### Mean Absolute Error

The Arithmetic mean of the positive magnitude of all the absolute Errors is called mean absolute error.

It is given by

### Relative Error Or Fractional Error

The ratio of the mean absolute error to the true value of measured quantity is called relative error.

### Percentage Error

The relative error expressed in percent is called percentage error.