If the median of the following data is 50, then find p. Class Frequency 0 - 20 10 20 - 40 7 40 - 60 16 60 - 80 p 80 - 100 8 Options: A . &nbsp6 B . &nbsp7 C . &nbsp8 D . &nbsp9

If the median of the following data is 50, then find p. ClassFrequency0

Question

If the median of the following data is 50, then find p.

\begin{matrix} Class & Frequency 0 - 20 & 10 20 - 40 & 7 40 - 60 & 16 60 - 80 & p 80 - 100 & 8 \end{matrix}

Options:

A . 6

B . 7

C . 8

D . 9

Answer: Option D
:
D

\begin{matrix} Class & Frequency & C u m u l a t i v e F r e q u e n c y 0 - 20 & 10 & 10 20 - 40 & 7 & 17 40 - 60 & 16 & 33 60 - 80 & p & 33+p 80 -100 & 8 & 41+p \end{matrix}

Since median is 50, median class is 40-60.
Using

M e d i a n = l + [\frac{\frac{n}{2} - c f}{f}] \times h

H e r e, n = 41 + p,

⟹ \frac{n}{2} = \frac{(41 + p)}{2}

N o w, 50 = 40 + [\frac{\frac{(41 + p)}{2} - 17}{16} \times 20]

⟹ 10 = [\frac{\frac{(41 + p - 34)}{2}}{16} \times 20]

⟹ 10 = [\frac{(7 + p)}{16 \times 2} \times 20]

Simplifying, we get

\frac{(7 + p)}{16} = 1

7 + p = 16

p = 9

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