Q. 83.7( 16 Votes )

# The median of the

Answer :

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.

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