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If the median of the following frequency distribution is $32.5$ and sum of all frequencies is $40$, then find the values of $f_1$ and $f_2$:
Class Interval: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$
Frequency: $3$ $f_1$ $9$ $12$ $6$ $f_2$ $2$
If the median of the following frequency distribution is $32.5$ and sum of all frequencies is $40$, then find the values of $f_1$ and $f_2$:
Class Interval: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$
Frequency: $3$ $f_1$ $9$ $12$ $6$ $f_2$ $2$
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Sol. Correct table (I Mark)
Median = $32.5 \therefore$ Median class is $30 - 40$ (II Mark)
$32.5 = 30 + \frac{20 - (12 + f_1)}{12} \times 10$ (III Mark)
$\Rightarrow f_1 = 5$ (IV Mark)
$\therefore 32 + f_1 + f_2 = 40$
$\therefore f_2 = 3$ (V Mark)
Median = $32.5 \therefore$ Median class is $30 - 40$ (II Mark)
$32.5 = 30 + \frac{20 - (12 + f_1)}{12} \times 10$ (III Mark)
$\Rightarrow f_1 = 5$ (IV Mark)
$\therefore 32 + f_1 + f_2 = 40$
$\therefore f_2 = 3$ (V Mark)