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

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Solution

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

$Mean, \bar{x} = A + \{h \times \frac{\sum (f_{i} \times u_{i})}{\sum f_{i}}\}$
$= 125 + \{50 \times \frac{85}{180}\} = 125 + 23.61 = 148.61$
Hence, the mean of the given frequency is 148.61.

OR
We have:

Therefore,
$Mean, \bar{x} = \frac{\sum (f_{i} \times u_{i})}{\sum f_{i}}$
$\Rightarrow \frac{(1700 + 35 p)}{(80 + p)} = 24$
$\Rightarrow (1700 + 35 p) = 1920 + 24 p$
$\Rightarrow 11 p = (1920 - 1700) = 220$
$\Rightarrow p = \frac{220}{11} = 20$
Hence, the value of p is 20.

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