The frequency distribution of the marks obtained by students in a...

The class marks (midpoints) $x_i$ for the given intervals are $10, 20, 30, 40$.

The corresponding frequencies $f_i$ are $20, 30, 30, 20$.

Total number of students, $N = \sum f_i = 20 + 30 + 30 + 20 = 100$

Calculating the sum of $f_i x_i$:
$\sum f_i x_i = (20 \times 10) + (30 \times 20) + (30 \times 30) + (20 \times 40)$
$\sum f_i x_i = 200 + 600 + 900 + 800 = 2500$

Arithmetic mean $\bar{x} = \dfrac{\sum f_i x_i}{N} = \dfrac{2500}{100} = 25$

Answer: $25$