Question

The arithmetic mean of the following frequency distribution is 50.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	16	p	30	32	14

Find the value of p.

Answer 1

Class	Mid value $\left(x_i\right)$	Frequency $\left(f_i\right)$	$\left(x_i\times f_i\right)$
0-10	5	16	80
10-20	15	$p$	15$p$
20-30	25	30	750
30-40	35	32	1120
40-50	45	14	630
		$\sum f_i=p+92$	$\sum f_i{x}_i=15p+2580$

$$\begin{gathered} \therefore \mathrm{Mean},\overline{\mathrm{x}}=\frac{\sum f_i{x}_i}{\sum f_i} \\ =\frac{15p+2580}{p+92} \\ \mathrm{Now},\frac{15p+2580}{p+92}=50 \\ \Rightarrow 50p+4600=15p+2580 \\ \Rightarrow 35p=-2020 \\ \Rightarrow p=-\frac{404}{7}\left(\mathrm{frequency}\mathrm{}\mathrm{cannot}\mathrm{}\mathrm{be}\mathrm{}\mathrm{negative}\right) \end{gathered}$$

So, there is an error in question.