# 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.

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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