Question

The mean of the following frequency distribution is 27, find the the value of p.
Class:
0-10
10-20
20-30
30-40
40-50
Frequency:
8
p
12
13
10

Answer 1

STEP DEVIATION METHOD:

Step deviation method is used in the cases where the deviation from the assumed mean 'A' are multiples of a common number. If the values of ‘di’ for each class is a multiple of ‘h’ the calculation become simpler by taking ui= di/h = (xi - A )/h

Here, h is the class size of each class interval.

★★ Find the class marks of class interval. These class marks would serve as the representative of whole class and are represented by xi.  

★★ Class marks (xi)  = ( lower limit + upper limit) /2

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn

MEAN = A + h ×(Σfiui /Σfi) , where ui =  (xi - A )/h

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfiui = 17 - p ,  Σfi = 43 + p

Let the assumed mean, A = 25,  h = 10

Given : Mean = 27

MEAN = A + h ×(Σfiui /Σfi)

27 = 25 + 10 [(17 - p)/(43 + p)]

27 - 25 = 10 [(17 - p)/(43 + p)]

2/10 = [(17 - p)/(43 + p)]

⅕ =  [(17 - p)/(43 + p)]

43 + p = 5(17 - p)

43 + p = 85 - 5p  

p + 5p = 85 - 43

6p = 42

p = 42/6

p = 7

Hence, the value of p is  7 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The value of p is 7.

Step-by-step explanation :

Step deviation method -

We use step deviation method in case where the deviation are multiples of a common number from the assumed mean.

We can calculate it by taking

$u_{i}=\frac{d_i}{h}=\frac{x_{i}-A}{h}$

$Mean=A+h\times\frac{\Sigma f_{i}u_i}{\Sigma f_i}$

where h is the class size of each class interval.

Frequency Distribution Table -

Let the assumed mean be .

$\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6}Class & x_i & f_i & d_i & u_i & f_{i}u_i\\ \cline{1-6}0-10 & 5 & 8 & -20 & -2 & -16\\ \cline{1-6}10-20 & 15 & 0 & -10 & -1 & -p\\ \cline{1-6}20-30 & 25 & 12 & 0 & 0 & 0\\ \cline{1-6}30-40& 35 & 13 & 10 & 1 & 13\\ \cline{1-6}40-50 & 45 & 10 & 20 & 2 & 20\\ \cline{1-6} & & \Sigma f_{i}=43+p & & & \Sigma f_{i}u_{i}=17-p\\ \cline{1-6}\end{tabular}$

Since, mean -

$\implies A+h\times\frac{\Sigma f_{i}u_i}{\Sigma f_i}$

$\implies 27=25+10\times\frac{(17-p)}{(43+p)}$

$\implies 27-25=10\times\frac{(17-p)}{(43+p)}$

$\implies\frac{2}{10}=\frac{(17-p)}{(43+p)}$

$\implies\frac{1}{5}=\frac{(17-p)}{(43+p)}$

$\implies 43+p=5(17-p)$

$\implies 43+p=85-5p$

$\implies p+5p=85-43$

$\implies 6p=42$

$\implies p=7$