If the mean of the following distribution is 24, find the value of a :

Marks	Number of students
0 - 10	7
10 - 20	a
20 - 30	8
30 - 40	10
40 - 50	5

We construct the following table :

$\therefore \text{Mean} = \dfrac{∑f$iyi}{∑f_i} \\[1em] \Rightarrow 24 = \dfrac{810 + 15a}{30 + a} \\[1em] \Rightarrow 24(30 + a) = 810 + 15a \\[1em] \Rightarrow 720 + 24a = 810 + 15a \\[1em] \Rightarrow 24a - 15a = 810 - 720 \\[1em] \Rightarrow 9a = 90 \\[1em] \Rightarrow a = 10.

Hence, the value of a = 10.