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.

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
Frequency	10	20	?	40	?	25	15

Given: Median = 35 & N = 170

Assume

Σf_i = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and C_f = 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 C_f = 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.