Question 3: Define the terms error and uncertainty. Explain different types of errors?

## Error

Error is the difference between the true value of the quantity being measured and the measured value by the experimenter.

It is quite difficult to eliminate all types of errors and uncertainties in a measurement.

## Uncertainty

Uncertainty is the part of the reported value that characterizes the range of values within which the true value is asserted (asserted means sure, certain) to lie. An uncertainty estimate should address errors from all possible effects (that is, systematic and random). Therefore, it is the most appropriate mean of expressing accuracy of the result.

## Types of error

There are three types of errors in the measurement.

### (1) Personal Error

The error due to carelessness, improper knowledge about the instrument or incorrect reading of the scale by an experimenter is called personal error.

The remedy is the experimenter should have proper knowledge about the instrument of measurement and should take proper care in the measurement of the quantities.

### (2) Systematic Error

The error due to faulty apparatus and poor calibration or zero error in the instrument is called systematic error.

A positive error is subtracted from the reading of the faulty instrument and added in case of negative error.

### (3) Random Error

The error due to repeated measurements of the same quantity under the same conditions that results in different values is called random error.

The error can arise due to the change in temperature or some other unknown reason. Maintaining strict control conditions in the lab, repeating the measurement several times and taking the mean value of these measurements can minimize this error.

TOTAL error is the combination of systematic and random errors.