Q. 73.9( 31 Votes )

# Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Answer :

Median(given) = 24, 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 = 24 (as already mentioned in the question)

24 lies between 20 - 30 ⇒ Median class = 20 - 30

∴ l = 20, h = 10, f = x, N/2 = (55 + x)/2 and C_{f} = 30

Median is given by,

⇒

⇒

⇒ 24 – 20 = (10x – 50)/2x

⇒ (4)(2x) = 10x – 50

⇒ 8x = 10x – 50

⇒ 10x – 8x = 50

⇒ 2x = 50

⇒ x = 25

Thus, the unknown frequency is 25.

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