Accuracy Precision Measurement - A Complete Guide

We will discuss precision meaning, accurate meaning, Accuracy and precision definition, precise meaning, and accurate meaning, accuracy, and precise meaning
Precise meaning:-. What is the meaning of precise? To be precise meaning a specific value that may or may not be accurate.
Accurate meaning:- We can define accurately as exact value or near the true value.

What is accuracy and precision, let’s discuss in detail.

Accuracy and precision:-What is accuracy? and what is precision? In common language the phrase accuracy and precision convey almost the same meaning but in science the same is not true; a measurement may give precise measurement but it can be quite inaccurate at the same time. So, what is accuracy in physics and what is precision in physics? And also what is accuracy and precision in chemistry. To understand the distance between terms, let’s take an example in which a person doing shooting practice and is allowed to shoot six bullets and aiming at Bull’s eye in a target frame consisting of circular regions of varying radius.

• Center is bull’s eye
• Bullet shots.

In fig a, the shots hit the target frame in the outer circle and are scattered widely with respect to each other. Hence, it is a case of low precision and low accuracy. In fig b, the bullets are marked in the outer circular region away from target but are clustered in a very small region. Thus it is a case of low accuracy and high precision. Further in fig c, although the bullet spots are scattered widely with respect to each other, yet these spots are in an internal circular region, very close to the Bull’s eye therefore,it is a case of low precision and high accuracy. And finally in figure d the spots are clustered with respect to each other and simultaneously these are very close to the Bull’s eye. Therefore it is a case of high precision and high accuracy.

So, now we understand what is meant by the term accuracy and what is meant by precision. So, we can define accuracy and precision as

Accuracy is defined as, ‘’ the extent up to which an observe value agrees with the true value of a quantity (or closeness of measured value to true value is) is known as it’s accuracy’’

And the instrument which gives repeated readings close to the true value of the physical quantity under consideration, is an accurate instrument. On the other hand, we can define precise as the precision of an observed value tells what resolution the quantity is measured. Thus, the measured values which are very close to each other (may or may not be close to the true value) are precise values and an instrument which gives a tight cluster of repeated results is a precise instrument.

Precise meaning in tamil is துல்லியமான. Accuracy meaning in tamil is திட்பநுட்பம். Accuracy meaning in gujarati is ચોકસાઈ

Also read -

• NCERT Solutions for Class 11 Physics
• NCERT Solutions for Class 12 Physics
• NCERT Solutions for All Subjects

Accuracy vs Precision:- We can distinguish accuracy and precision as

“ the precision of an observed value tells what resolution the quantity is measured”.

“The extent up to which an observed value agrees with the true value of a quantity is known as its accuracy.”

The accuracy of the measurement is determined by absolute error. The accuracy depends upon significant figures .Measurement which is close to true value is known as accuracy.

Accuracy Precision of an instrument and errors in measurement:-

Accuracy and Precision in measurement:- The accuracy of an instrument

depends more on systematic error (for example calibration error, zero error, etc,.) present in it rather than some other factors. It can be improved by applying a proper correction. Higher the accuracy , smaller the error.

Thus, an error gives the indication of accuracy. On the other hand, precision depends on random errors. precision of an instrument is defined as degree of freedom from random errors Therefore, it can be eradicated. Moreover, higher is the precision, larger is the number of significant figures. Thus, the precision gives the indication of the number of significant figures in a measurement. Precision of measurement depends on the least count of the instruments. Some precision measurement instruments are screw gauge, vernier callipers, and dial indicator etc.

Error in the measurement:- In the measurement taken during an experiment in the laboratory, two types of errors are present; errors of observation and error present in the instrument. Uncertainty of measurement is technically called an error. Error is always expressed in percentage.

Mainly, errors are two types:

(i) Systematic errors:- These errors occur constantly in an experiment repeated under identical conditions.These errors come into existence by virtue of a definite rule.Therefore, once the rule which governs these errors is identified these errors can be eradicated by applying proper corrections to the result obtained.

(ii) Random errors:-These arise due to (i) small changes in the condition of the experiment and (ii) incorrect judgement of the observer in taking readings.

Methods of minimising random errors:- The random error can be minimised by taking the arithmetic mean of a large number of readings of the same quantity.

NCERT Physics Notes :

• NCERT Notes class 11 physics
• NCERT Notes class 12 physics
• NCERT Notes for all subject

Absolute error:- The magnitude of the difference between the true value (or value obtained after taking arithmetic mean) of the measured quantity and the individual measured value is called an absolute error.

∴ An absolute error = True value ~ measured value

Let a1, a2, a3, ….an are the measured values of the physical quantity, the absolute error.

?a1 = ¯a ~ a1

?a2 = ¯a ~ a2

…………………………...

?an = ¯a ~ an

Where ¯a is a mean value or true value.

Mean absolute Error:- The arithmetic mean of the absolute error of the different measurement is called mean absolute error.

Mean absolute error, ¯?a = 丨?a1丨+ 丨?a2丨+ 丨?a3丨/ n

¯?a = 1/n ∑ 丨?ai丨

Accuracy and precision examples:-

A screw gauge is a precise instrument because it gives precise measurement of the diameter of the wire but a thermometer is an accurate instrument because it gives an accurate measurement of temperature. So, the accuracy example is the thermometer and the precision example is screw gauge.

• which of the following measurement is most precise
• 6.00 mm
• 6.00 cm
• 6.00 m
• 60.00 m

Correct option is 6.00 mm

• which of the following instruments is most accurate
• 0.006 mm
• 6.00 mm
• 60.00 mm
• 6.0 mm

Correct option is 0.006 mm

What is meant by measurement or what is the definition of the measurement:-Measurement can be defined as numbers linked to the physical quantity which can be measured size, capacity, time, etc,. Concept of measurement is important in our daily life.

Need of measurement:- But what is the need of measurement? Lord Kelvin once said, “ when you can measure what you are speaking about and express it in numbers, you know about it; but when you cannot express it in numbers, your knowledge is of meagre and unsatisfactory kind. For example, if you want to buy milk but you don’t know how much? Because you don't know the quantity of milk. If you want to tell someone how much time you studied or played then how can you tell them if you do not know that in which quantity time can be measured but if you know that you can easily tell them i studied or played for one hour. So, we measure length in meters or kilometers, weight in kg, velocity in speed/second, etc,. These are the examples of measurement.

Also Read :

• NCERT solutions for Class 11 Physics Chapter 2 Units and Measurement
• NCERT notes Class 11 Physics Chapter 2 Units and Measurement
• NCERT Exemplar Class 11 Physics Solutions Chapter 2 Units and Measurements

How to calculate the accuracy and precision:-

The reliability of two voltmeters A and B of range 3V each, is examined against a standard voltage source of emf 1.018 V . The voltage of source is measured five times and the corresponding reading of voltmeters in all five sets are recorded as under in a tabular form :

1. Which voltmeter gives precise measurement and which has higher accuracy? Explain.
2. What may be the actual cause due to which reading of voltmeter B is greater than2 V in all five sets though emf of source is 1.018 only?

Solution. (1) The variation in the reading shown by voltmeter A = 1.09 - 1.01 = 0.08 V

And the variation in the reading of voltmeter B =2.05 - 2.01 = 0.04 V

Since the variations in the readings shown by voltmeter B are smaller compared to that of voltmeter A, which means the values recorded by voltmeter B are very close to each other, hence voltmeter B has greater precision.

Now, the arithmetic mean of readings shown by voltmeter A = 1.01 + 1.07 + 1.09 + 1.08 / 5V = 1.06 V

And the arithmetic mean of the readings of voltmeter B = 2.02 + 2.04 + 2.03 + 2.05 + 2.01 / 5 V = 2.03 V

Since, the average reading of voltmeter A is close to the true value (1.018 V) therefore, voltmeter A is more accurate.

(2) Since, the source voltage is 1.018 V, therefore any correct voltmeter cannot record the potential difference of the force greater than this value. However, it is possible only when there is some error in the meter. Prima Facie it seems that voltmeter B has a zero error of 1 V. If this error is eradicated by applying proper corrections, it would give an accurate as well as precise readings.

2. In an experiment of a simple pendulum, a student made several observations for the period of oscillation. His readings turned out to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. Find (i) mean period of oscillation, or most accurate valueof time period. (ii) absolute error in each reading, (iii) mean absolute error, (iv) fractional error and (v) percentage error.

Solution. (i) The mean period of oscillation of the pendulum is

T = 2.63 + 2.56 + 2.42 + 2.71 + 2.80 / 5 s =

13.12 / 5 s = 2.624 s = 2.62 s. (rounded off to second decimal place)

(ii) Taking 2.62 s as the true value, the absolute errors ( true value - measured value ) in the five readings taken are :

2.62 s - 2.63 s = - 0.01 s, 2.62 s - 2.56 s = 0.06 s, 2.62 s - 2.42 s = 0.20 s, 2.62 - 2.71 s = - 0.09 s, 2.62 s - 2.80 s = - 0.18 s.

(iii) The (maximum) mean absolute error is

(?T) max = 0.01 + 0.06 + 0.20 + 0.09 + 0.18 / 5 sec

= 0.54 / 5 s = 0.108 s = 0.11 s. (rounded off to second decimal place)

(iv) The maximum fractional error is

(?T/T)max = 0.11 s/ 2.62 s = 0.0419 = 0.04.

(v) The percentage error is

(?T/T) max multiply 100 = 0.04 x 100 = 4%

The value of T should be written as

T =(2.62 +- 0.11) s.

As the arithmetic mean of all the absolute errors is 0.11 s, there is already an error in the first decimal place. Hence, there is no point in giving the period up to second decimal place . We should, more correctly, write

T = (2.6 +- 0.1) s.

Also check-

• NCERT Exemplar Class 11th Physics Solutions
• NCERT Exemplar Class 12th Physics Solutions
• NCERT Exemplar Solutions for All Subjects