Page 68 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Income (Rs.) Number (f) Cumulative Frequency
upto 10000 30 30
Unit 4: Research Problem
10000-14999 125 155
20000-24999 50 205
25000-29999 30 235
Notes
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 = LLM 1 i 
0 0  D  D 
 1 2 
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 = 10,000     5,000
d  95 75 

substitute the values

 95 
= 10000 +   170   = 5000 = 1000+2794 = 12794

Conclusion: Majority have the income of 12794. This is how statistical techniques are used in
MR application.

Median

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

 N 
  – C.F. 
M = LM 2  i
d d
FM d
M = Lower limit of median class
d
CF = Cumulative frequency for the class just below the median class.

Fm = Frequency of the median class.
d
i = Size of the class interval of median class.
In the table N = 300 N/2 = 150. The class containing the 150th person is the median class.
Substitute the value, we get median M = 21568
d

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