Question

The mean of the following frequency distribution is 24. Find the value of p.

Marks	0-10	10-20	20-30	30-40	40-50
Number of students	15	20	35	p	10

Answer 1

Class	Frequency $\left(f_i\right)$	Mid Values $\left(x_i\right)$	$(f_i\times x_i)$
0-10	15	5	75
10-20	20	15	300
20-30	35	25	875
30-40	p	35	35 p
40-50	10	45	450
	$\sum f_i=80+p$		$\sum (f_i\times x_i)=1700+35p$

$$\begin{gathered} \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \Rightarrow \text{24 =}\frac{1700+35p}{80+p}[\because \text{Mean=24}] \\ \Rightarrow \text{1920+24}p=1700+35p \\ \Rightarrow \text{11}p=220 \\ \Rightarrow p=20 \\ \therefore p=20 \end{gathered}$$