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

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$5$	$7$	$12$	$10$	$8$	$6$	$2$

(N/A) $1$. Mean: The total frequency $N = 50$. The midpoints $(x_i)$ are $35, 45, 55, 65, 75, 85, 95$. The sum $\sum f_i x_i = (5 \times 35) + (7 \times 45) + (12 \times 55) + (10 \times 65) + (8 \times 75) + (6 \times 85) + (2 \times 95) = 175 + 315 + 660 + 650 + 600 + 510 + 190 = 3100$. Mean $\bar{x} = \frac{\sum f_i x_i}{N} = \frac{3100}{50} = 62$.
$2$. Median: $N/2 = 25$. The cumulative frequencies are $5, 12, 24, 34, 42, 48, 50$. The median class is $60-70$. Median $= l + \left( \frac{N/2 - cf}{f} \right) \times h = 60 + \left( \frac{25 - 24}{10} \right) \times 10 = 60 + 1 = 61$.
$3$. Mode: The modal class is $50-60$ (highest frequency $12$). Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 50 + \left( \frac{12 - 7}{2(12) - 7 - 10} \right) \times 10 = 50 + \left( \frac{5}{24 - 17} \right) \times 10 = 50 + \frac{50}{7} \approx 50 + 7.14 = 57.14$.