Question

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

Class interval	0-50	50-100	100-150	150-200	200-250	250-300
Frequency	17	35	43	40	21	24

Or, The mean of the following frequency distribution is 24. Find the value of P.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	15	20	35	p	10

Answer 1

Let us assumed mean A be 125; h = 50
For calculating the mean, we prepare the table as shown below.

$\mathrm{Mean},\overline{\mathrm{x}}=\mathrm{A}+\left\{\mathrm{h}\times \frac{\sum \left({\mathrm{f}}_{\mathrm{i}}\times {\mathrm{u}}_{\mathrm{i}}\right)}{\sum {\mathrm{f}}_{\mathrm{i}}}\right\}$
$=125+\left\{50\times \frac{85}{180}\right\}=125+23.61=148.61$
Hence, the mean of the given frequency is 148.61.

OR
We have:

Therefore,
$\mathrm{Mean},\overline{\mathrm{x}}=\frac{\sum \left({\mathrm{f}}_{\mathrm{i}}\times {\mathrm{u}}_{\mathrm{i}}\right)}{\sum {\mathrm{f}}_{\mathrm{i}}}$
$\Rightarrow \frac{\left(1700+35p\right)}{\left(80+p\right)}=24$
$\Rightarrow \left(1700+35p\right)=1920+24p$
$\Rightarrow 11p=\left(1920-1700\right)=220$
$\Rightarrow p=\frac{220}{11}=20$
Hence, the value of p is 20.