Tutorial Examples of Arithmetic Mean


Examples of Arithmetic Mean


   


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

Distance (Km)

Number of Persons


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.

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 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.

Marks

Frequency

Solution:

Direct Method

Short-Cut
Method

Step-Deviation
Method

Marks

Total


(1) Direct Method:
or Marks
(2) Short-Cut Method:
Where
Marks
(3) Step-Deviation Method:
Where

Marks


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