If the mean of the following distribution is 27, then the value of p is :

Class	Frequency
0 – 10	8
10 – 20	p
20 – 30	12
30 – 40	13
40 – 50	10

1. 6

2. 7

3. 9

4. 11

By formula,

$\Rightarrow \text{Mean} = \dfrac{\sum fx}{\sum f} \\[1em] \Rightarrow 27 = \dfrac{1245 + 15p}{43 + p} \\[1em] \Rightarrow 27(43 + p) = 1245 + 15p \\[1em] 1161 + 27p = 1245 + 15p \\[1em] \Rightarrow 27p - 15p = 1245 - 1161 \\[1em] 12p = 84 \\[1em] \Rightarrow p = \dfrac{84}{12} \\[1em] \Rightarrow p = 7.$

Hence, option 2 is the correct option.