Explain Absolute Error, Relative Error and Percentage Error.
Explain Absolute Error, Relative Error and Percentage Error.
$(a)$ Absolute Error:
The magnitude of the difference between the individual measurement and the true value of the quantity is called the absolute error of the measurement.
It is denoted by $|\Delta a|$.
In absence of any other method, we consider arithmetic mean as true value.
Consider physical quantity ' $a$ '. Its measurement be $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ Average value,
$\therefore a_{\text {mean }}=\frac{a_{1}+a_{2}+a_{3}+\ldots a_{n}}{n}$ OR
$\sum^{n} a_{i}$
$=\frac{i=1}{n} \text { where, } i=1,2,3, \ldots, n$
$(b)$ Absolute error in measurement
$\Delta a_{1}=a_{1}-a_{\text {mean }}$
$\Delta a_{2}=a_{2}-a_{\text {mean }}$
$: \quad: \quad:$
$\Delta a_{n}=a_{n}-a_{\text {mean }}$
$\Delta a$ may be positive or negative.
Average absolute error is denoted by $(\Delta a)_{\text {mean }}$
$=\frac{\left|\Delta a_{1}\right|+\left|\Delta a_{2}\right|+\ldots\left|\Delta a_{n}\right|}{n}$
$=\frac{\sum_{i=1}^{n}\left|\Delta a_{i}\right|}{n}$
where, $i=1,2,3, \ldots, n$
Physical quantity is represented as,
$a=a_{\text {mean }} \pm(\Delta a)_{\text {mean }}$
$\text { OR } a_{\text {mean }}-\Delta a_{\text {mean }} \leq a \leq a_{\text {mean }}+\Delta a_{\text {mean }}$
Similar Questions
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A$ : A spherical body of radius $(5 \pm 0.1)$ $mm$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\,\%$.
Reason $R$ : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below on :
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A$ : A spherical body of radius $(5 \pm 0.1)$ $mm$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\,\%$.
Reason $R$ : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below on :
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