Question

Find the mean of the following distribution, using the step deviation method:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	12	13	10	8

Or, the mean of the following distribution is 78. Find the value of P.

Class	50-60	60-70	70-80	80-90	90-100
Frequency	8	6	12	11	p

Answer 1

Let the assumed mean A be 25; h = 10
For calculating the mean, we prepare the table given below.

$\mathrm{Mean},\overline{\mathrm{x}}=\mathrm{A}+\left\{\mathrm{h}\times \frac{\sum \left({\mathrm{f}}_{\mathrm{i}}\times {\mathrm{u}}_{\mathrm{i}}\right)}{\sum {\mathrm{f}}_{\mathrm{i}}}\right\}$
$=25+\left\{10\times \frac{0}{50}\right\}=25+0=25$
Hence, the mean of the given frequency is 25

OR
We have:

Therefore,
$\mathrm{Mean},\overline{\mathrm{x}}=\frac{\sum \left({\mathrm{f}}_{\mathrm{i}}\times {\mathrm{u}}_{\mathrm{i}}\right)}{\sum {\mathrm{f}}_{\mathrm{i}}}$
$\Rightarrow \frac{\left(2665+95p\right)}{\left(37+p\right)}=78$
$\Rightarrow \left(2665+95p\right)=2886+78p$
$\Rightarrow 17p=\left(2886-2665\right)=221$
$\Rightarrow p=\frac{221}{17}=13$
Hence, the value of p is 13.