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Accuracy Precision Error Measurement

Accuracy Precision Error Measurement

Team Careers360Updated on 02 Jul 2025, 05:09 PM IST

Measurement is defined as the most important thing that we can apply in science as well as mathematics. But when we are talking about measurement and they occur, some of the accurate measurements and some of the errors also occur in the measurement that is termed as precision. Even if we want to compare any weight or anything else such as the quantity we use the term such as measurement. But every measurement is not accurate. It carries some of the accuracies in it and that is termed as the error in the measurement.

This Story also Contains

  1. Define error
  2. Types of Error:
  3. What is Accuracy
Accuracy Precision Error Measurement
Accuracy Precision Error Measurement

Define error

Error is the difference between the measured value and the actual value.

For example, if we want to calculate the value of quantity by the instrument or the device and it is done by two operators then it is not necessary that both operators give the same result. The difference between the two measurements that are taken by the two different operators is termed to be an error.

Commonly Asked Questions

Q: What is the concept of "error bars" in graphical representations of data?
A:
Error bars are graphical representations of the variability of data. They indicate the uncertainty in a reported measurement. On a graph, they extend from each data point, showing the range within which the true value is likely to fall, based on the measurement's uncertainty.
Q: What is the concept of "measurement uncertainty" and how is it different from error?
A:
Measurement uncertainty quantifies doubt about the measurement result. It's an estimate of a range of values that is likely to include the true value. Error, on the other hand, is the difference between a measured value and the true value. Uncertainty acknowledges that the true value is unknown.
Q: How does the concept of "tolerance" relate to measurement accuracy?
A:
Tolerance is the permissible deviation from a specified value. It defines the acceptable range of variation in a measurement or manufactured part. While related to accuracy, tolerance is more about defining acceptable limits rather than the closeness to the true value.
Q: How does hysteresis affect measurement accuracy?
A:
Hysteresis is the dependence of a system's output on its history of inputs. In measurements, it can cause different readings when approaching a value from different directions. This can introduce errors and affect accuracy, particularly in mechanical or magnetic measuring devices.
Q: How does the concept of "outliers" relate to measurement accuracy and precision?
A:
Outliers are data points that significantly differ from other observations. They can affect both accuracy and precision. Outliers may indicate a genuine extreme value, a measurement error, or a problem with the measurement process. Proper handling of outliers is crucial for maintaining data integrity.

Types of Error:

1. Gross error :

It is a kind of error that occurs due to the mistake that is made by humans by breeding and recording the instrument. This is the most common error that occurs during any kind of measurement if we are using any kind of titration then it may be possible then we are not using the buret in a proper way so the gross error occurs. To avoid gross errors you must take proper care regarding the data.

2. Random errors :

As the name suggests these errors occur in a random way not because due to any proper condition these are termed to be random errors. These types of errors can arise due to unpredictable changes in the temperature and the voltage supplied during an experiment.

3. Systematic error:

These types of errors are further classified into three different groups :

Environmental Errors: Environmental errors are those errors that are affected by the external conditions of the environment on the measurement. This type of error occurred due to external conditions such as changes in temperature and pressure.

Observational Error: when the experiment is not set up with the proper care and the Observer is doing carelessness in such a type of condition observation error occurs.

Instrumental Errors: This type of error arises due to the wrong calibration of the measuring instrument. When the equipment used is faulty then changes in the reading may occur and the zero error is a very common type of error that occurs in the instrumental errors.

Commonly Asked Questions

Q: How does systematic error differ from random error?
A:
Systematic errors are consistent, repeatable deviations from the true value, often due to faulty equipment or flawed methodology. Random errors are unpredictable fluctuations in measurements due to various uncontrollable factors. Systematic errors affect accuracy, while random errors affect precision.
Q: What is the difference between absolute and relative error?
A:
Absolute error is the difference between the measured value and the actual value, expressed in the same units as the measurement. Relative error is the absolute error divided by the actual value, often expressed as a percentage. Relative error allows for comparison between measurements of different magnitudes.
Q: What is meant by "propagation of errors" in calculations?
A:
Propagation of errors refers to how uncertainties in individual measurements combine to affect the uncertainty of a calculated result. When performing calculations with measured values, the uncertainties in each measurement contribute to the overall uncertainty of the final result.
Q: What is the importance of reporting uncertainties with measurements?
A:
Reporting uncertainties with measurements is crucial because it provides information about the reliability and limitations of the data. It allows others to assess the quality of the measurements, make informed decisions based on the data, and properly compare results from different experiments or sources.
Q: What is the relationship between resolution and precision in measurements?
A:
Resolution refers to the smallest change in a quantity that an instrument can detect. While high resolution can contribute to precision, they are not the same. An instrument with high resolution allows for more precise measurements, but other factors like random errors also affect overall precision.

What is Accuracy

Accuracy is defined as the difference between the mean value of a particular performed experiment or experimental value of the measurement and the True value of that measurement that is used to calculate a result of a given experiment. Another meaning of accuracy is to find true value.

So mathematically it can be written as,

Accuracy = Mean value - True value.

When we talk about accuracy we find out that the difference between the mean value and true is much smaller than the accuracy is found to be much larger in an experimental result.

Example of Accurate vale :

We have been given a compound that contains 50g of nitrogen mean value. Now you are advised to perform two different experiments and find out the concentration of the Iron elements that are present in the compound.

You find out that through method A the true concentration of iron is found to be 20g and in experiment B the true concentration is found to be 10hg.

Solution:

Accuracy = Mean value - True value

Method A = 50g - 20g = 30g

Method B = 50g - 10g = 40g

Define Precision

Precision is defined as a quantity in measurement that shows how closely two or many measurements of the same quantity are in terms of one another. It is calculated by finding out the difference between a measured value and the arithmetic mean value for many different measurements.

Mathematically it can be written as

Precision = Individual Value – Arithmetic Mean

Example of Precision

As a result we find out the extent of agreement between the repeated measurements that have been provided for the same quantity. It is observed that if the difference between the individual values of repeated measurements is smaller, the precision is greater.

We are taking an example to understand the concept of concept is

A speedometer given. Let us first consider that Car A runs at 50km/hr. If the speedometer which you are using for the purpose of measuring speed shows the value of 48.8 or 48.9 or 49 then the measurements of these types are considered precise but not accurate. Now if the speedometer shows 49.7 or 50.5 then these values will be considered accurate but not precise.

Commonly Asked Questions

Q: What's the difference between accuracy and precision in measurements?
A:
Accuracy refers to how close a measurement is to the true value, while precision refers to how consistent or reproducible measurements are. An accurate measurement is close to the actual value, whereas precise measurements are close to each other but not necessarily to the true value.
Q: Can a measurement be precise but not accurate?
A:
Yes, a measurement can be precise but not accurate. This occurs when repeated measurements are consistent with each other (high precision) but are systematically off from the true value (low accuracy). For example, if a scale consistently measures 1 kg too high, it's precise but not accurate.
Q: How does rounding affect the accuracy and precision of a measurement?
A:
Rounding can affect both accuracy and precision. Excessive rounding can reduce accuracy by moving the value further from the true value. It also reduces precision by limiting the number of significant figures, potentially obscuring small but important variations in measurements.
Q: How does calibration relate to accuracy in measurements?
A:
Calibration is the process of adjusting an instrument to provide results that are accurate compared to a known standard. Regular calibration helps maintain accuracy by correcting for systematic errors that may develop over time due to wear, environmental factors, or other influences.
Q: How does the concept of uncertainty relate to measurements?
A:
Uncertainty in measurements represents the range within which the true value is likely to fall. It acknowledges that no measurement is perfect and quantifies the doubt about the result. Uncertainty is often expressed as a range (±) or a percentage.

Frequently Asked Questions (FAQs)

Q: How does the concept of "measurement accuracy class" relate to instrument selection?
A:
Measurement accuracy class is a standardized way of expressing the accuracy of measuring instruments. It typically indicates the maximum permissible error as a percentage of the full scale or measured value. Understanding accuracy classes helps in selecting appropriate instruments for specific measurement tasks.
Q: What is meant by "type A" and "type B" uncertainties in measurements?
A:
Type A uncertainties are those evaluated by statistical methods, typically from repeated measurements. Type B uncertainties are evaluated by other means, such as manufacturer specifications, calibration certificates, or expert judgment. Both types contribute to the overall measurement uncertainty.
Q: How does the concept of "measurement uncertainty budget" contribute to understanding overall accuracy?
A:
A measurement uncertainty budget is a detailed breakdown of all sources of uncertainty in a measurement. It includes factors like instrument accuracy, environmental effects, and operator variability. By quantifying each source, it provides a comprehensive understanding of the overall measurement uncertainty.
Q: How does the concept of "measurement accuracy ratio" relate to instrument selection?
A:
The measurement accuracy ratio is the ratio of the measurement process accuracy to the tolerance of the characteristic being measured. A higher ratio indicates a more capable measurement system relative to the required tolerance. It's a crucial factor in selecting appropriate measuring instruments for specific tasks.
Q: What is meant by "measurement range" and how does it affect accuracy?
A:
Measurement range is the span between the minimum and maximum values that an instrument can measure. Using an instrument within its specified range is crucial for accuracy. Measurements at the extremes of the range may be less accurate due to non-linearity or other factors.
Q: What is meant by "measurement bias"?
A:
Measurement bias is a systematic error that causes measurements to consistently deviate from the true value in a particular direction. It affects the accuracy of measurements and can be due to factors like improper calibration, consistent misreading, or flawed methodology.
Q: How does the concept of "uncertainty budget" relate to measurement accuracy?
A:
An uncertainty budget is a comprehensive list of all sources of uncertainty in a measurement process. It helps in understanding and quantifying the overall uncertainty in a measurement result, allowing for a more accurate assessment of the measurement's reliability.
Q: How does digital resolution affect measurement accuracy?
A:
Digital resolution, the smallest increment a digital instrument can display, can affect perceived accuracy. While high resolution allows for finer measurements, it doesn't necessarily improve accuracy. The last digit may imply more precision than the instrument actually provides.
Q: How does the choice of reference point affect measurement accuracy?
A:
The choice of reference point can significantly impact measurement accuracy. An inappropriate or unstable reference point can introduce systematic errors. For example, measuring the height of a mountain using sea level as a reference point requires accounting for tidal variations.
Q: How does the concept of "drift" affect long-term measurement accuracy?
A:
Drift refers to a gradual, unintended change in instrument readings over time. It can be caused by factors like component aging or environmental changes. Drift affects long-term accuracy and necessitates regular calibration to maintain measurement reliability.
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