Examples of Arithmetic Mean
Example:
The following data shows distance covered by people to perform their routine jobs.
Distance (Km)





Number of People





Calculate the arithmetic mean by stepdeviation method; also explain why it is better than direct method in this particular case.
Solution:
The given distribution is grouped data and the variable involved is distance covered, while the number of people represents frequencies.
Distance Covered in (Km)

Number of People

Mid Points























Total



Now we will find the arithmetic mean as
Here
, , and
Km
Explanation:
Here from the mid points () it is very clear that each mid point is a multiple of and there is also a gap of from mid point to midpoint, i.e. class size or interval (). Keeping this in mind, we should use the stepdeviation method instead of direct method.
Example:
The following frequency distribution showing the marks obtained by students in statistics at a certain college. Find the arithmetic mean using (1) direct method (2) shortcut method (3) stepdeviation.
Marks








Frequency








Solution:
Direct Method

ShortCut
Method 
StepDeviation
Method 

Marks
































































Total





(1) Direct Method:
or Marks
(2) ShortCut Method:
Where
Marks
(3) StepDeviation Method:
Where
Marks