Question

Find the missing values where median and mode of the following distribution is given 33.5 and 34 , respectively, choose which of the following is a correct pair.

Class Internal		Frequency
	0-10		4
	10-20		16
	20-30		?
	30-40		?
	40-50		?
	50-60		6
	60-70		4

Column - I		Column - II
I	$I^{\text{st }}$ frequency	P	50
II	II ${}^{\text{nd }}$ frequency	Q	68
III	III ${}^{\text{rd }}$ frequency	R	70
		S	40
		T	100

• A. $I-Q,II-S$
• B. $I-Q,III-S$
• C. III-R, III-P
• D. III-T, III $-S$

Answer 1

Answer: (D)

Let missing frequency $(20-30)=x$
Missing frequency $(30-40)=y$
And missing frequency $(40-50)=230-(4+$ $16+(x+y+6+4)$ $=200-x-y$

$\text{ Median }=l_1+\frac{\frac{N}{2}-f_0}{f}\times (l_2-l_1)$
$33.5=30+\frac{115-(20+x)}{y}\times (40-30)$
$y(33.5-30)=(11.5-20-x)10$
$3.5y=1150-200-10x$
$10x+3.5y=950$
$\text{ Mode }=l_1+\frac{f_1-f_0}{2f_1-f_0-f_2}\times (l_2-l_1)$
$34=20+\frac{y-x}{2y-2(-200-x-y)}\times (30-20)$
$4(3y-200)=10(y-x)$
$10x+2y=800$
Subtracting equation (ii) from equation (i), we get
$1.5y=150$
$\Rightarrow y=100$
Equality value of $y$ in eq(l), we get
$10x+3.5(100)=950$
$10x=950-350$
$\Rightarrow x=60$
So, third frequency $=200-x-y=200-60$ $-100=40$