Find the values of$x_1$and $x_2$if the distribution's median is 28.5:

Class interval	Frequency (f)
0-10	5
10-20	$x_1$
20-30	20
30-40	15
40-50	$x_2$
50-60	5
	$\sum _{ \mathrm{f}}$ = 60

To calculate the median from the following interval data, we must first compute the cumulative frequencies.

Because the class widths are unequal in this case, we don't need to adjust the interval frequencies. We will use the cumulative frequency to find the median class and then apply the formula to find the median of a data set. 

Median $=l+\frac{\frac{n}{2}-c.f}{f}\times h$

Given:- $\sum _{ \mathrm{f}}=60$

$\therefore x_1+x_2+45=60$

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

Given: - Median =28.5

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

Where L is the lower limit of class 20-30

f is the frequency of class 20-30,

w is the width of the class

C is the cumulative frequency of the previous class and $N=\Sigma F$ $\Rightarrow L=20,\frac{N}{2}=\frac{60}{2}=30,C=x_1+5,w=30-20=10,f=20$

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

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

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

$x_1=8$From eq.(i),we ge$x_1+x_2=15$

$8+x_2=15$

$x_2=7$

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