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 the absence of any other method,we consider the arithmetic mean as the true value.
Consider a physical quantity '$a$'. Let its measurements be $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$. The average value is:
$a_{\text{mean}} = \frac{a_{1}+a_{2}+a_{3}+\ldots+a_{n}}{n} = \frac{1}{n} \sum_{i=1}^{n} a_{i}$
The absolute error in each measurement is:
$\Delta a_{1} = a_{1} - a_{\text{mean}}, \Delta a_{2} = a_{2} - a_{\text{mean}}, \ldots, \Delta a_{n} = a_{n} - a_{\text{mean}}$.
The mean absolute error is:
$(\Delta a)_{\text{mean}} = \frac{|\Delta a_{1}| + |\Delta a_{2}| + \ldots + |\Delta a_{n}|}{n} = \frac{1}{n} \sum_{i=1}^{n} |\Delta a_{i}|$.
$(b)$ Relative Error:
The ratio of the mean absolute error to the mean value of the quantity is called the relative error.
Relative Error $= \frac{(\Delta a)_{\text{mean}}}{a_{\text{mean}}}$.
$(c)$ Percentage Error:
When the relative error is expressed in percentage,it is called the percentage error.
Percentage Error $= \frac{(\Delta a)_{\text{mean}}}{a_{\text{mean}}} \times 100\%$.