Example (4):
The following data shows distance covered by persons to perform their routine jobs.
Distance (Km) 




Number of Persons 




Calculate Arithmetic Mean by StepDeviation Method; also explain why it is better than direct method in this particular case.
Solution:
The given distribution belongs to a grouped data and the variable involved is ages of “distance covered”. While the “number of persons” Represent frequencies.
Distance Covered in (Km) 
Number of Persons 
Mid Points 






















Total 




Now we will find the Arithmetic Mean as
Where
, , and
Km
Explanation:
Here from the mid points () it is very much clear that each mid point is multiple of and there is also a gap of from mid point to midpoint i.e. class size or interval (). Keeping in view this, we should prefer to take method of StepDeviation instead of Direct Method.
Example (5):
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 
StepDeviation 

Marks 































































Total 







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