Question

Write any two merits of the arithmetic mean.

Answer 1

Hint: First we need to know the meaning of Arithmetic mean, where the major merit of this method is the calculation of arithmetic mean is easy as it requires basic knowledge of Maths such as addition, subtraction, multiplication, and division of numbers.

Complete step-by-step answer:
Arithmetic Mean is the most common measurement of central tendency. According to the layman, the mean of data represents an average of the given collection of the data. It is equivalent to the sum of all the observations of a given data divided by the total number of observations.
The mean of data for n values in a set of data namely ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ is given by,
$\bar x = \dfrac{{{x_1} + {x_2} + {x_3} + \ldots + {x_n}}}{n}$
For calculating the arithmetic when the number of observations along with the frequency of observation is given such that ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ are the recorded observation and ${f_1},{f_2},{f_3}, \ldots ,{f_n}$ are the corresponding frequencies of the observation,
$\bar x = \dfrac{{{f_1}{x_1} + {f_2}{x_2} + {f_3}{x_3} + \ldots + {f_n}{x_n}}}{{{f_1} + {f_2} + {f_3} + \ldots + {f_n}}}$
The above Arithmetic mean formula is expressed as $\dfrac{{\sum {{f_i}{x_i}} }}{{\sum {{f_i}} }}$.
When we search for the advantages of arithmetic mean, we need to remember two points:
The calculation of arithmetic mean is easy as it requires basic knowledge of Maths such as addition, subtraction, multiplication, and division of numbers.
All the values of data are taken into consideration while calculating arithmetic mean.

Note: The other merits of arithmetic mean are:-
The meaning of the arithmetic mean can be easily understood such as the value or unit or cost per unit etc.
The value of the arithmetic mean is always definite as it is defined rigidly.
It can be widely used in advanced statistical analysis as it has competency for further algebraic operation.
A comparison of the data of two or more groups can be easily done through arithmetic mean.