# Error and accuracy in measurement

## Error and accuracy in measurement

All measurements have some limitations of accuracy. The accuracy of the measurement depends on the skill of the observer and the instruments used. Suppose a meter scale is graduated in centimeter and millimeter. If we want to measure the length of this book we will get the result probably up to 0.1cm accurately. Accuracy may be reduced in case of measuring the length of a house because the scale is to be used several times for measuring the full length. Every time the position of the front edge of the scale has to be a marker on the floor. This increases the source of error thus increasing the probability of errors.

The accuracy of measurement is as important as the measurement itself. So, the observer should mention the degree of accuracy of the result with the result of the experiment. Let the length of this book be 26.0cm ± 0.1cm. Here the symbol ± means that the real length of the book is between 25.9cm and 26.1cm. Here 0.1cm is the uncertainty or error of measurement.

Generally, there are three types of errors in measurement.

There are :

a) Random error

b) Instrumental error

c) Personal error

**a) Random error:**The error for which irrelevant occur in measured results by measuring constant quantities. Several times is random error. The word random itself implies that the error cannot be guessed earlier and the expected value will be zero. This is because measured values move around the accurate value and the average value of the errors should be zero if the value of the quantity is measured by the same instrument. The random error will be included as much as many times the scale is used to measure the floor. Each time the front edge marking on the floor falls a little back and forth of the accurate mark. Another random error takes place with the measurement when the meter scale is placed at the previous marking (slightly error position) as the back edge starts from the back and forth position. The final result may be very much high or low due to random error. It is impossible to avoid random error but this error can be reduced by precautionary measurement. To minimize the random error average of the frequent measurement is to be taken.

**b) Instrumental error:**We need instruments for experimental measurement in physics. The error with the instrument is called instrumental error. For example, if the zero marking of the main scale is not super-imposition with the zero marking vernier then the result of measurement will not be accurate. This kind of error is known as instrumental error. Similarly, if the indicator needle of ammeter or voltmeter is not super-imposition with the zero marking then there remains error with the instrument. The instrumental error has to be determined before starting the experiment. Finally, the actual reading has to be obtained by subtracting this error from the reading.

**c) Personal error:**We have to take various readings during the experiment. The error that an experimenter makes during the experiment is called personal error. The error with the position of the observer, observing any mark or any calculation is also said to be a personal error. For example, there will be an error while measuring the length of a rod if the super-imposition of the edge of a rod with a definite mark of the scale is observed obliquely instead of perpendicular position. There will be an error in reading when we cannot observe which division of circular scale is in super-imposition with the linear scale of a time per screw gauge. Similarly, we cannot find accurate if there is a mistake in counting the oscillation number while determining the time-period of a pendulum. All these are known as personal errors. We have to take the reading properly and carefully to avoid these errors.