Q. 163.7( 4 Votes )

The median value for the following frequency distribution is 35 and the Sum of all the frequencies is 170. Using the formula for median, find the missing frequencies.

Answer :

Given: Median = 35 & N = 170

Assume


Σfi = N = Sum of frequencies,


h = length of median class,


l = lower boundary of the median class,


f = frequency of median class


and Cf = cumulative frequency


Lets form a table, where x and y are the unknown frequencies.



Median = 35 (as already mentioned in the question)


35 lies between 30 - 40 Median class = 30 - 40


l = 30, h = 10, f = 40, N/2 = (110 + x + y)/2 = 170/2 = 85 and Cf = 30 + x


Median is given by,





35 – 30 = (55 – x)/4


5 × 4 = 55 – x


20 = 55 – x


x = 55 – 20 = 35 …(i)


And given that N = 170


110 + x + y = 170


x + y = 170 – 110


x + y = 60 …(ii)


Substituting x = 35 in eq.(ii),


35 + y = 60


y = 60 – 35 = 25


Thus, the unknown frequencies are x = 35 and y = 25.


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