Find the mean,median,and mode of the following frequency distribution:

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Frequency	$4$	$6$	$8$	$12$	$10$	$5$	$5$

(N/A) $1$. Mean: $\sum f_i = 50$. Mid-points $(x_i)$: $5, 15, 25, 35, 45, 55, 65$. $\sum f_i x_i = (4 \times 5) + (6 \times 15) + (8 \times 25) + (12 \times 35) + (10 \times 45) + (5 \times 55) + (5 \times 65) = 20 + 90 + 200 + 420 + 450 + 275 + 325 = 1780$. Mean $\bar{x} = \frac{1780}{50} = 35.6$.
$2$. Median: $N/2 = 25$. Cumulative frequencies: $4, 10, 18, 30, 40, 45, 50$. Median class is $30-40$. $l=30, f=12, cf=18, h=10$. Median $= l + \left( \frac{N/2 - cf}{f} \right) \times h = 30 + \left( \frac{25 - 18}{12} \right) \times 10 = 30 + \frac{70}{12} = 30 + 5.83 = 35.83$.
$3$. Mode: Modal class is $30-40$ (highest frequency $12$). $l=30, f_1=12, f_0=8, f_2=10, h=10$. Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 30 + \left( \frac{12 - 8}{24 - 8 - 10} \right) \times 10 = 30 + \left( \frac{4}{6} \right) \times 10 = 30 + 6.67 = 36.67$.