Common Errors in Measurement

The objective of every experiment is to determine the physical quantity as accurately as possible. However, every measurement consists of some errors which may occur due to the observer, the instrument used, or both. Errors can also occur due to small changes in the conditions of the experiment or due to many factors which are inherent in the experiment. The measured value of a quantity deviates somewhat from its actual value due to such errors.

Errors in Measurement

Experimental research and technology both are based on measurements. Every measurement made with a measuring instrument results in a specific degree of uncertainty. This uncertainty is called an error. The difference between the actual value of a quantity and estimated value of that quantity is called errors in measurements. An error can be positive or negative.

Therefore, the error is given as

Error=Measured value-Actual Value

Types of Errors in Measurements

There are three types of errors in measurements which are given here.

1. Systematic Errors
2. Random Errors
3. Gross Errors

Systematic Errors

The type of error that always affects the results of an experiment in the same direction, that is, makes the result obtained always larger or always smaller than the actual value. This is called systematic error. In fact, all the instrumental errors are systematic errors. When measurements are made with a scale at a different temperature than that at which it was calibrated, a systematic error is introduced.

There are following types of systematic errors which are given here.

1. Instrumental Errors
2. Personal Errors
3. Errors due to some external changes (like temperature change, pressure change, etc)
4. Errors occurs due to the imperfection

Random Errors

The results of multiple measurements of the same quantity by the same observer under similar conditions differ slightly from each other. The instrument can be good and sensitive, the observer can be very careful, however, such small differences in the results usually occur. A clear cause (reason) for such errors cannot be determined. Their sources are not known and also uncontrollable. Such errors are purely random in nature and are called random errors or accidental errors. 

The error that occurs randomly and the causes of which are unknown and undetermined is termed as random error.

Random errors in a measurement system are due to random and unpredictable fluctuations in the conditions of experiments.

Gross Errors

Gross errors or human errors arise basically due to human errors or one can also say that they are physical errors. For example, a person takes an incorrect reading or measurement while using an instrument. Incorrect data is recorded and this leads to a human error or gross error. Gross error or human error can be avoided by being careful and making sure the measurement you take is correct.

Sources of Error in measurement

There are many sources of error in measurement in which some of the important sources are given here.

1. Errors are produced by instruments.
2. Errors are produced by human mistakes.
3. Errors occur due to change in temperature, pressure, height, etc.

Proportional Error and Percentage Error

The ratio of error of observation to the observed reading (measurement) is termed as proportional error. When the proportional error is multiplied by 100 (hundred) or represents in percent, then the proportional error is termed as percentage error. Proportional error is also known as relative error or fractional error.

proportional error=error/observed value

percentage error=error/observed value*100

Least Count

Least count of an instrument is the lowest measurement which can be measured with that instrument. If the value of least count is small, then the dimension can be measured smaller and more accurately.

Consider an example, when a tape measure has 18 divisions, then the least count of the tape is 18. As the least count of a measuring device becomes small, it can make more accurate and precise measurements. A measuring instrument like a micrometer or digital Calliper has a lower least count as compared to a standard ruler. This allows it to measure in smaller increments and is therefore more accurate. 

Least count is directly related to the precision. The smaller the least count number, the more accurate the instrument. For example, the least count of the mechanical Vernier 0.02, but for electronic vernier the least count is 0.01. Hence, the electronic Vernier is more accurate than mechanical vernier because it can determine the dimensions up to 0.01 mm.

Least count formula

Least count is determined by a formula which is given here.

Least count=Known interval/number of division

Conclusion

The difference between the actual value of a quantity and estimated value of that quantity is called errors in measurements.

the error is given as

Error=Measured value-Actual Value

There are three types of errors in measurements which are given here.

1. Systematic Errors
2. Random Errors
3. Gross Errors

The error that occurs randomly and the causes of which are unknown and undetermined is termed as random error.

When measurements are made with a scale at a different temperature than that at which it was calibrated, a systematic error is introduced.

The ratio of error of observation to the observed reading (measurement) is termed as proportional error.

Least count of an instrument is the lowest measurement which can be measured with that instrument.

Least count=Known interval/number of division