Question

Following table gives frequency distribution of amount of bonus paid to the workers in a certain factory.

Bonus paid (in Rs.)	Below 500	Below 600	Below 700	Below 800	Below 900	Below 1000	Below 1100
No. of workers	4	12	24	41	51	58	60

Find median amount of bonus paid to the workers.

• A. $801.27$ Rs.
• B. $812.27$ Rs.
• C. $846.27$ Rs.
• D. $735.29$ Rs.

Answer 1

Answer: (D)

$735.29$ Rs.

Consider the following table to calculate median:

$ci$	$fi$	$cf$
<500	4	4
500-600	12-4=8	12
600-700	24-12=12	24
700-800	41-24=17	41
800-900	51-41=10	51
900-1000	58-51=7	58
1000-1100	60-58=2	60

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

Here,

Class Interval $c=100$

$N=\Sigma f_i=60$

$\frac{N}{2}=30$

$\Rightarrow$ Median class $=700-800$

$\Rightarrow$Frequency of median class$f_m=17$

Lower boundary of median class $l=700$

previous cumulative frequency of median class $cf=24$

$\therefore$ Median $=700+\frac{(\frac{60}{2}-24)}{17}\times 100$

$\therefore$ Median $=700+\frac{\left(6\right)}{17}\times 100$

$\therefore$ Median $=735.29$

Hence. option $D$ is correct.