Errors in Measurement, Types, Calculation, Example
Table of Contents
The advancement of science and technology is crucial without the availability of accurate calculated values to provide convincing arguments. A technical investigation is actually founded on theory, which is only supported by established, quantified principles. The investigator is able to differentiate between various intensities of the calculated characteristics and can instantly assign a fixed value to events. Different kinds of measurement errors play a significant role in reducing the statement effort and increasing the result’s independence. An overview of the various types of errors in measurement is provided in this article, along with a calculation formula and an illustration.
What are Errors in Measurement?
The discrepancy between calculated worth and actual worth is referred to as an error or fault. It’s not necessary for them to obtain the same results, for instance, if the two machinists use the same instrument to find measurement errors. However, there will be a tiny difference between the two measurements, which is referred to as an error. To understand the concept of measurement errors, one must first recognize the two terms that describe the error, namely the measured value and the true value. It is impossible to determine the “true value” through experimental means; it can be thought of as the average value of an infinite number of calculated values. This value can be described as the expected value of true value which can be established by taking numerous calculated values throughout experimentation.
Types of Errors in Measurement
The following types of errors in measurement are typically categorized based on the sources from which they may arise. Below, these are explained in more detail.
- Systematic Errors
- Gross Errors
- Random Errors
1. Systematic Errors
These types of systematic errors are generally categorized into three types which are explained below in detail.
- Observational Errors
- Environmental Errors
- Instrumental Errors
The fault analysis of the instrument reading, one of the many sources of observational errors, may result in these errors. For instance, a voltmeter’s indicator will occasionally tune itself slightly above the scale’s surface. As a result, a mistake occurs unless the witness’s image is precisely above the indicator. Extremely precise meters with reflected scales are available to help reduce the parallax error.
Environmental errors will occur as a result of the measuring instruments’ environment. These kinds of mistakes frequently result from temperature, force, moisture, dirt, vibration, or an electrostatic or magnetic field. The following are the corrective actions taken to get rid of these undesirable effects.
- The preparation should be finished to remain the situations as stable as achievable.
- By the instrument which is at no cost from these results.
- With these methods which remove the result of these troubles.
- By applying the computed modifications.
Instrumental errors will happen due to some of the following reasons
An inherent limitation of Devices
Devices naturally contain these errors because of their mechanical design. These could occur as a result of both instrument operation and instrument computation. These kinds of mistakes cause people to mistakenly believe they can learn very little or very much. For instance, if the measuring device uses a delicate spring, it offers a high level of measurement accuracy. These will occur in the apparatus as a result of a reduction in friction or hysteresis.
Abuse of Apparatus
The machinist made a mistake that led to the instrument’s error. A superior tool applied to an unintelligent process could produce a significant outcome. For instance, misuse of the equipment could result in tool breakdown, poor early modification, and extremely high resistance. Improper observation of these may not result in long-term damage to the device, but instead only results in faults.
Effect of Loading
The measurement work done by the device will cause the most common type of this error to occur. For instance, if the voltmeter is connected to a high-resistance circuit, the circuit will read falsely, and if it is connected to a low-resistance circuit, the circuit will read accurately. In either case, the voltmeter will load the circuit. Meters will be used wisely to combat the fault that is brought on by this effect. As an example, a voltmeter should be used because the ammeter-voltmeter method will result in an extremely high resistance value when calculating low resistance.
2. Gross Errors
Gross errors include actual computation and recording errors as well as errors in analysis equipment. These types of mistakes typically occur during experiments, where the researcher may study or record a value that is different from the actual one, possibly as a result of a limited view. Error types are predictable due to human concern, though they can be predicted and fixed.
These types of errors can be prohibited by the following couple of actions:
- Careful reading as well as a recording of information.
- multiple readings of the instrument from various operators. Secure agreements between parties with different understandings ensure that all major mistakes are eliminated.
3. Random Errors
This type of error is almost always present in measurements and is caused by oscillations in the experimenter’s interpretation of the apparatus reading or in the analysis of the apparatus measurement. These kinds of errors manifest as different results for apparently the same frequent measurement, which can be anticipated by contrasting and condensing many measurements.
The Measurement Errors Calculation
The calculation of measurement errors does not imply that a dimension is inaccurate. As a result, the apparatus causes the device measurement to be inaccurate. Absolute error, relative error, and percentage error are the three categories into which these errors fall.
The absolute error can be defined as the variation between the values of actual and measured.
Absolute error = |VA-VE|
Percentage error (%) = (|VA-VE|/VE) x 100
Relative Error = Absolute error/actual value
Here, VA stands for the measured value while VE stands for the exact value.
Measurement Errors Example
A length of 5.8 feet was calculated, but the actual length was 5.72 feet. Calculate the percentage and absolute errors.
Here, VA = 5.8 feet and VE =5.62 feet
Absolute error = |VA-VE| =| 5.8-5.72| = 0.08ft
Percentage error (%) = (|VA-VE|/VE) x 100 = |0.08/5.62| x 100 = 1.423 %
Relative Error = |VA-VE|/ VE = 0.08/5.8 = 0.013
The above article gives a brief idea regarding sources of errors in measurement