The median of the following data is 16. Find the missing frequencies a and b if the Total of frequencies is 70. [CBSE 2013]

Class	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
Frequency	12	A	12	15	b	6	6	4

Given: Median = 16 & N = 70

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 is the unknown frequency.

Median = 16 (as already mentioned in the question)

16 lies between 15 - 20 ⇒ Median class = 15 - 20

∴ l = 15, h = 5, f = 15, N/2 = (55 + a + b)/2 and C_f = 24 + a

Median is given by,

⇒

⇒

⇒ 16 – 15 = (7 – a + b)/6

⇒ 6 = 7 – a + b

⇒ a – b = 1 …(i)

And given that N = 70

⇒ 55 + a + b = 70

⇒ a + b = 15 …(ii)

Solving equations (i) & (ii), we get

(a – b) + (a + b) = 1 + 15

⇒ 2a = 16

⇒ a = 8

Substituting a = 8 in eq.(i),

8 – b = 1

⇒ b = 7

Thus, the unknown frequencies are a = 8 and b = 7.