Question

Following shows the distribution of monthly expenditure (in Rs.) done by households in a certain village on electricity.
Find median expenditure done by households on electricity per month.

Monthly expenditure	150 - 225	225 - 300	300 - 375	375 - 450	450 - 525	525 - 600	600 and above
No. of households	65	171	196	75	53	26	14

• A. Rs. $324.49$
• B. Rs. $354.49$
• C. Rs. $364.49$
• D. Rs.$400.49$

Answer 1

Answer: (A)

Rs. $324.49$

Consider the following table, to calculate median:

$ci$	$f_i$	$cf$
150-225	65	65
225-300	171	65+171=236
300-375	196	236+196=432
375-450	75	432+75=507
450-525	53	507+53=560
525-600	26	560+26=586
>600	14	586+14=600

Median $=l+\frac{(\frac{N}{2}-cf)}{f_m}\times c$

Here,

Class Interval $c=75$

$N=\Sigma f_i=600$

$\frac{N}{2}=300$

$\Rightarrow$ Median class $=300-375$

$\Rightarrow$Frequency of median class$f_m=196$

Lower boundary of median class $l=300$

previous cumulative frequency of median class $cf=236$

$\therefore$ Median $=300+\frac{(\frac{600}{2}-236)}{196}\times 75$

$\therefore$ Median $=300+\frac{\left(64\right)}{196}\times 75$

$\therefore$ Median $=324.489\Rightarrow 324.49$

Hence. option $A$ is correct.