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Example (4):
The following data shows distance covered by  persons to perform their routine jobs.
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Number of Persons
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Calculate Arithmetic Mean by Step-Deviation 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.
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Distance Covered in (Km)
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Number of Persons
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Mid Points
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Total
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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 mid point i.e. class size or interval ( ). Keeping in view this, we should prefer to take method of Step-Deviation 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) Short-Cut Method (3) Step-Deviation.
Solution:
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Direct Method
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Short-Cut
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Step-Deviation
Method
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Marks
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Total
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(1) Direct Method:
 or  Marks
(2) Short-Cut Method:
 Where 
 Marks
(3) Step-Deviation Method:
 Where  
 Marks
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