The median of the following frequency distribution is $46$ and the total frequency is $230$. Find the missing frequencies $x$ and $y$.
Class $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Frequency $12$ $30$ $x$ $65$ $y$ $25$ $18$

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(N/A) Given total frequency $N = 230$.
Sum of frequencies: $12 + 30 + x + 65 + y + 25 + 18 = 230$
$150 + x + y = 230 \implies x + y = 80$ ---(Equation $1$)
Since the median is $46$,the median class is $40-50$.
Here,$l = 40$,$h = 10$,$f = 65$,$N = 230$,and cumulative frequency of the class preceding the median class $cf = 12 + 30 + x = 42 + x$.
Using the median formula: $\text{Median} = l + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h$
$46 = 40 + \left( \frac{115 - (42 + x)}{65} \right) \times 10$
$6 = \left( \frac{73 - x}{65} \right) \times 10$
$6 \times 6.5 = 73 - x$
$39 = 73 - x \implies x = 34$.
Substituting $x = 34$ in Equation $1$: $34 + y = 80 \implies y = 46$.
Thus,$x = 34$ and $y = 46$.

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