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

Class	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$
Frequency	$10$	$15$	$30$	$20$	$15$	$8$	$2$

(A) $1$. Mean: $\sum f_i = 100$. Mid-points $(x_i)$: $25, 75, 125, 175, 225, 275, 325$. $\sum f_i x_i = 250 + 1125 + 3750 + 3500 + 3375 + 2200 + 650 = 14850$. Mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{14850}{100} = 148.5$.
$2$. Median: $N/2 = 50$. Cumulative frequencies: $10, 25, 55, 75, 90, 98, 100$. Median class is $100-150$. $l=100, cf=25, f=30, h=50$. Median $= l + \left( \frac{N/2 - cf}{f} \right) \times h = 100 + \left( \frac{50-25}{30} \right) \times 50 = 100 + \frac{25 \times 50}{30} = 100 + 41.67 = 141.67$.
$3$. Mode: Modal class is $100-150$ $(f_1=30, f_0=15, f_2=20)$. Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 100 + \left( \frac{30-15}{60-15-20} \right) \times 50 = 100 + \left( \frac{15}{25} \right) \times 50 = 100 + 30 = 130$.