Accuracy Precision Error Measurement

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.

JEE Main 2025: Physics Formula | Study Materials | High Scoring Topics | Preparation Guide

JEE Main 2025: Syllabus | Sample Papers | Mock Tests | PYQs | Study Plan 100 Days

NEET 2025: Syllabus | High Scoring Topics | PYQs

This Story also Contains

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

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.

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.

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.