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The median of the following data is 16. Find the missing frequ

Question

The median of the following data is 16. Find the missing frequencies a and b, if the total frequency is 70.
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

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The median of the following data is 16. Find the missing frequencies a and b, if the total frequency is 70.

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

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Text solutionVerified

Here:

N = 70

N /2 = 35

Median

= 16

, Median class

= 15 - 20

So,

I = 15, h = 5, f = 15

and

x f = x f

of preceding class i.e.

24 + a

We know,
Median

= 1 + ⎩ ⎨ ⎧ h \times \frac{( \frac{N}{2} - c f )}{f} ⎭ ⎬ ⎫

Substitute all the value in the above formula, we get

16 = 15 + {5 \times (35 - 24 - a) /15}

\Rightarrow 16 = 15 + (11 - a) /3

a = 8

Now,

70 = 55 + a + b

70 = 55 + 8 + b

\Rightarrow b = 7

so, missing frequincies are

8

and

7

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Question Text	The median of the following data is 16. Find the missing frequencies a and b, if the total frequency is 70.
Answer Type	Text solution:1
Upvotes	151