Errors in Measurement

Introduction

Measurement is the muse of all experimental science. In an experiment, we may get a different value than the true value due to either faulty equipment, carelessness, or other reasons. This causes an error in measurement. The result of each measurement by any measuring device contains some uncertainty. This uncertainty is called an error. Errors in measuring systems occur because of inescapable faults within the measuring instrument and limitations of the human eye.

How is Error in Measurement Calculated?

The difference between the true value and the measured value is called an error in measurement.

Error = true value – measured value

Below are the 3 types of errors in measurement:

1. Systematic error
2. Random error
3. Gross error

Systematic Error

Systematic errors are those errors that tend to be in one line path, either positive or negative. Systematic errors are often minimised by refining experimental techniques, selecting better instruments, and removing personal bias.

Random errors

These are the errors that are desultory and are therefore arbitrary regarding sign and size. These can arise due to arbitrary and changeable variations in experimental conditions (e.g. variations in temperature, voltage force, the mechanical climate of experimental set-ups, etc), particular (unprejudiced) errors by the bystander taking readings, etc. For example, when the same person repeats the same experiment, it is likely that he or she may get a different reading each time. 

Gross Error

Gross errors or outliers, are errors away from arbitrary faults or methodical faults. They are frequently large and arbitrary by description. They are generally caused by unforeseen changes in the current physical circumstances, by system faults, or by human fault. 

Error Calculation

There are three different ways to calculate errors in measurement. They are: 

Absolute Error

Absolute error is the difference between the measured value and the real value. The expression for absolute error is E absolute = |x measured − x accepted|. For example, suppose we’re measuring the length of an eraser, and the factual length of the eraser is 35 mm and the measured length is 34.13 mm. In this case, the absolute error = Factual length − measured length, i.e, (35-34.13) mm = 0.87 mm. 

Mean absolute error is the computation mean of all absolute crimes. It’s represented by Δamean.

Relative Error

It represents the rate of the absolute error of the dimension to the accepted dimension. Relative error can be represented as; E relative = E absolute/ x accepted. Relative error formula = | measured value − factual value|.  The factual value would be x0 and the measured value would be x, if the absolute error of the dimension is – ∆x.xr = (x0-x)/ x0 = ∆ x/ x0. Here, xr is the relative error. If we take the eraser example mentioned above, the actual length of the eraser is 35 mm and the absolute error = (35 – 34.13) mm = 0.87 mm. In this case, the relative error = absolute error/actual length  = 0.87/35 which is 0.02485. 

Percentage Error

Percentage error is analogous to relative error. Only in this case, the error is converted to a percent value. The expression for percent error is percent of Error = | measured value − factual value|/ factual value ∗ 100. 

For example, a scale incorrectly measures a value of 14 cm when the factual dimension of the value is 10 cm. In this case, experimental value = 14 cm and factual value = 10 cm. This is how we’ll calculate the percentage error: Percent of Error = | measured value − factual value|/ factual value ∗ 100, i.e, (14-10)/ 10 * 100. So, the percentage error in this example is 40 %. 

Ways to Reduce Dimension Error: 

• Double-check all measures for delicacy.

• Double-check all formulas. 

• Make sure spectators and dimension takers are well trained. 

•  Make the dimension with the instrument that has the loftiest perfection. 

• Take the measures under controlled conditions. 

•  Use tools applicable to what’s being measured. 

•  Measure multiple times.

• If there is an outlier, find a justification for calling it an outlier in the foremost place.

• Average the result but append the scale.

Conclusion

The main intent of error analysis is to see whether the results of the trial agree with a theoretical prediction or results from other trials or not. Mainly, the evaluated performance of results agree with a theoretical prediction if the prediction lies within the range of experimental variations. The relative error is the rate of the mean absolute error ∆ mean to the mean value a mean of the volume measured. When the relative error is exhibited in percentage form, it’s called the percentage error.