Page 193 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes
Income ( ) Number (f) Cumulative Frequency
upto 10000 30 30
10000-14999 125 155
20000-24999 50 205
25000-29999 30 235
30000-34999 33 268
35000-49999 20 288
above 35000 12 300

In the above table, 125 is the modal class.
Mode can be calculated using the formula:

 D 
M 0 = LM 0  1   i
 D  D 2 
1
LM = Lower limit of modal class.
0
D = Difference between the frequency of modal class and the class immediately
1
preceding the modal class.
D = Difference between the frequency of the modal class and the class immediately
2
succeeding the modal class.
i = size of the modal class interval.

 95 
M d = 10,000     5,000
 95 75 

substitute the values

 95 
= 10000 +  
 170 
= 5000 = 1000+2794 = 12794
Conclusion: The majority have the income of 12,794. This is how statistical techniques are used
in MR application.

Median

Median lies precisely halfway between the highest and lowest values. It is necessary to arrange
the data into ascending or descending order before selecting the median value. For the ungrouped
data with an odd number of observations, the median would be the middle value. For an even
number of observations, the median value is half way between central value.
For a grouped data, the median is calculated using the formula:

 N 
   C.F  
M = LM 2  i
d d
fM d
M = Lower limit of median class.
d

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