Question

If the median of the distribution is $28.5$, find thevalues of $x_1$ and $x_2$

Class interval	Frequency
0-10	5
10-20	$x_1$
20-30	20
30-40	15
40-50	$x_2$
50-60	5
	Total $=$ 60

• A. $8,7$
• B. $9,7$
• C. $6,8$
• D. $7,9$

Answer 1

The correct option is A $8,7$

Answer:-

Class Interval	Frequency (F)	Cumulative frequency (C. F.)
0-10	5	5
10-20	$x_1$	5 + $x_1$
20-30	20	25 + $x_1$
30-40	15	40 + $x_1$
40-50	$x_2$	40 + $x_1+x_2$
50-60	5	45 + $x_1+x_2$
Total	60

Given:- $\Sigma F=60$

$\therefore x_1+x_2+45=60$

$\Rightarrow x_1+x_2=15⟶eq.\left(i\right)$

Given: - Median = $28.5$

Using media:- $L+\frac{\frac{N}{2}-C}{f}\times w$

Where $L$ is lower limit of class $20-30$

$f$ is frequency of class $20-30,$

$w$ is width of class

$C$ is cumulative frequency of previous class and$N$ = $\Sigma F$

$\Rightarrow$ $L=20$, $\frac{N}{2}=\frac{60}{2}$ = $30$, $C=x_1+5,$ $w=30-20=10$, $f=20$

$\Rightarrow M=20+\frac{30-(x_1+5)}{20}\times 10$

$28.5=20+\frac{25-x_1}{20}\times 10$

$8.5=\frac{25-x_1}{2}$

$x_1=8$

From eq. (i), we get

$x_1+x_2=15$

$8+x_2=15$

$x_2=7$

$\therefore$ value of $x_1\&x_2$ are $8$ and $7$ respectively.