Arithmetic Mean
Arithmetic mean is the most commonly used average or measure of the central tendency applicable only in case of quantitative data; it is also simply called the “mean”. Arithmetic mean is defined as:
“Arithmetic mean is a quotient of sum of the given values and number of the given values”.
Arithmetic mean can be computed for both ungrouped data (raw data: data without any statistical treatment) and grouped data (data arranged in tabular form containing different groups).
If is the involved variable, then the arithmetic mean of is abbreviated as of and denoted by . The arithmetic mean of can be computed with any of the following methods.
Method’s Name

Nature of Data


Ungrouped Data

Grouped Data


Direct Method



Indirect or
ShortCut Method 


Method of
StepDeviation 


Here
indicates value of the variable
indicates number of values of
indicates frequency of different groups
indicates assumed mean
indicates deviation from i.e,
indicates stepdeviation and indicates common divisor
indicates size of class or class interval in case of grouped data
indicates summation or addition
Example:
The oneway train fare of five selected BS students is recorded as follows , , , and . Calculate the arithmetic mean of the following data.
Solution:
Let train fare be indicated by , then







The arithmetic mean of , so we decide to use the abovementioned formula. From the given data, we have and . Placing these two quantities in the above formula, we get the arithmetic mean for the given data.
Example:
Provide the given distribution of the following frequency distribution of first year students of a particular college:
Age (Years)






Number of Students






Solution:
The given distribution is grouped data and the variable involved is ages of first year students, while the number of students represents frequencies.
Ages (Years)

Number of Students

















Total



Now we will find the arithmetic mean as years.
Example:
The following data shows the distance covered by people to perform their routine jobs.
Distance (Km)





Number of People





Solution:
The given distribution is grouped data and the variable involved is distance covered, while the number of people represents frequencies.
Distance (Km)

Number of People

Mid Points


















Total



Now we will find the arithmetic mean as Km.