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

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$5$	$27$	$58$	$20$	$10$

(N/A) $1$. Mean Calculation:
Class marks $(x_i)$: $5, 15, 25, 35, 45$.
Sum of frequencies $(\sum f_i)$ $= 5 + 27 + 58 + 20 + 10 = 120$.
Sum of products $(\sum f_i x_i)$ $= (5 \times 5) + (27 \times 15) + (58 \times 25) + (20 \times 35) + (10 \times 45) = 25 + 405 + 1450 + 700 + 450 = 3030$.
Mean $(\bar{x}) = \frac{\sum f_i x_i}{\sum f_i} = \frac{3030}{120} = 25.25$.
$2$. Median Calculation:
Cumulative frequencies $(cf)$: $5, 32, 90, 110, 120$.
$N/2 = 120/2 = 60$. The median class is $20-30$.
$l = 20, cf = 32, f = 58, h = 10$.
Median $= l + \left( \frac{N/2 - cf}{f} \right) \times h = 20 + \left( \frac{60 - 32}{58} \right) \times 10 = 20 + \left( \frac{280}{58} \right) \approx 20 + 4.83 = 24.83$.
$3$. Mode Calculation:
Modal class is $20-30$ (highest frequency $58$).
$l = 20, f_1 = 58, f_0 = 27, f_2 = 20, h = 10$.
Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 20 + \left( \frac{58 - 27}{116 - 27 - 20} \right) \times 10 = 20 + \left( \frac{31}{69} \right) \times 10 \approx 20 + 4.49 = 24.49$.