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

Class	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$
Frequency	$11$	$20$	$35$	$20$	$8$	$6$

(N/A) $1$. Mean: The class marks $(x_i)$ are $7.5, 12.5, 17.5, 22.5, 27.5, 32.5$. The sum of frequencies $(\sum f_i)$ is $100$. The sum of products $(\sum f_i x_i)$ is $(11 \times 7.5) + (20 \times 12.5) + (35 \times 17.5) + (20 \times 22.5) + (8 \times 27.5) + (6 \times 32.5) = 82.5 + 250 + 612.5 + 450 + 220 + 195 = 1810$. Mean $= \frac{\sum f_i x_i}{\sum f_i} = \frac{1810}{100} = 18.1$.
$2$. Median: $N/2 = 50$. The cumulative frequencies are $11, 31, 66, 86, 94, 100$. The median class is $15-20$. Median $= l + \left( \frac{N/2 - cf}{f} \right) \times h = 15 + \left( \frac{50 - 31}{35} \right) \times 5 = 15 + \left( \frac{19}{35} \right) \times 5 = 15 + \frac{19}{7} \approx 15 + 2.71 = 17.71$.
$3$. Mode: The modal class is $15-20$ (highest frequency $35$). Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 15 + \left( \frac{35 - 20}{2(35) - 20 - 20} \right) \times 5 = 15 + \left( \frac{15}{70 - 40} \right) \times 5 = 15 + \left( \frac{15}{30} \right) \times 5 = 15 + 2.5 = 17.5$.