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Accuracy, Precision and Error

Accuracy, Precision and Error

Author: Cecil McIntosh

The user of this packet should become familiar with the terms Accuracy, precision, Error, Systematic Error, and Random Error.

The user should also learn how to determine the accuracy of measurements by calculating the Absolute error, Relative error, or % error of measurements. The user should also learn how to determine the precision of measurements by calculating the deviation of individual measurements, and the average deviation of a collection of measurements.Furthermore, the user shall be able to identify erroneous measurements within a set, and identify the type of error in measurements - being either Systematic or Random Error.

This packet is an overview of the terms Accuracy and Precision, and the difference between them. This packet also discusses error, and gives examples of how error can affect the accuracy and precision of measurements, as well as showing how to categorize and identify error.

A few practice problems at the end give the user a chance to practice what they've learned in the lesson.

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Lesson 1 - Accuracy and Precision

Focus on Accuracy and Precision, and how to calculate the Accuracy and Precision of measurements.

Error - Types of Error and how they affect measurements

Terms and Equations

Terms And Equations


Accuracy  – How close a measurement is to the actual or expected value.

Precision – How close a set of measurements are to one another. 

Error –  The difference between the actual or expected value, and the measured value.

Absolute Error  =  Actual value – Measured value

Relative Error =  (Actual value – Measured value) / (Actual Value)

% Error –  Relative Error X 100%

Deviation – The difference between a measurement within a set and the mean of that set of measurements.

Deviation = Measurement  - Mean

Average Deviation -  The average of the Deviations of all measurements within a set.

Systematic Error – Error that impacts all or a large portion of measurements in a set uniformly, or by some type of trend.

Random Error – Error that occurs sporadically, without any sort of trend or predictability.

Offset error – is when a machine is not calibrated or set to measure zero, when the sample is at zero.

Multiplier error -  is an equipment malfunction where it amplifies changes in readings, or has a diminished sensitivity to change.

Source: Chemistry Quick Review of Experimental Error. Anne Marie Helmenstine, Ph.D.,,

Practice Problems