The below table shows that profit made by a group of shops in mall. Then the median is _____. P r o f i t p e r s h o p l e s s t h a n ( % ) 10 20 30 40 50 60 N o . o f s h o p s 12 30 57 77 94 100 Options: A . &nbsp 27.4 B . &nbsp 31.2 C . &nbsp 26.8 D . &nbsp 23.7

Answer: Option A : A Firstly, the cumulative frequency (CF) table is drawn. C . I C F F r e q u e n c y 0 − 10 12 12 10 − 20 30 18 20 − 30 57 27 30 − 40 77 20 40 − 50 94 17 50 − 60 100 6 T o t a l 100 n 2 = 100 2 = 50 C.F nearest to 50 and greater than 50 is 57. ∴ M e d i a n = l + ( n 2 − c f f ) × h Where l is lower class limit of median class. n is total number of observations. c f is the cumulative frequency of the class preceding the median class. f is the frequency of the median class and h is the class size. M e d i a n = 20 + ( 50 − 30 27 ) × 10 Median = 27.4

The below table shows that profit made by a group of shops in mall. Then the m

Question

The below table shows that profit made by a group of shops in mall. Then the median is _____.

$\begin{matrix} P r o f i t p e r s h o p l e s s t h a n (%) & 10 & 20 & 30 & 40 & 50 & 60 N o . o f s h o p s & 12 & 30 & 57 & 77 & 94 & 100 \end{matrix}$

Options:

A . 27.4

B . 31.2

C . 26.8

D . 23.7

Answer: Option A
:
A

Firstly, the cumulative frequency (CF) table is drawn.

$\begin{matrix} C . I & C F & F r e q u e n c y 0 - 10 & 12 & 12 10 - 20 & 30 & 18 20 - 30 & 57 & 27 30 - 40 & 77 & 20 40 - 50 & 94 & 17 50 - 60 & 100 & 6 T o t a l & 100 \end{matrix}$

$\frac{n}{2} = \frac{100}{2} = 50$

C.F nearest to 50 and greater than 50 is 57.

$∴ M e d i a n = l + (\frac{\frac{n}{2} - c f}{f}) \times h$
Where $l$ is lower class limit of median class.
$n$ is total number of observations.
$c f$ is the cumulative frequency of the class preceding the median class.
$f$ is the frequency of the median class and h is the class size.
$M e d i a n = 20 + (\frac{50 - 30}{27}) \times 10$