Question

The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find the missing frequency.
Class:
11−13
13−15
15−17
17−19
19−21
21−23
23−25
Frequency:
7
6
9
13
−
5
4

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  

Let the missing frequency be x .

From the table : Σfiui = x - 20 ,  Σfi = 44 + x  

Let the assumed mean, A = 18,  h = 2

Given : Mean = 18

MEAN = A + h ×(Σfiui /Σfi)

18 = 18 + 2[(x -20)/(44+x)]

18 - 18 =  2[(x -20)/(44+x)]

0 =  2[(x -20)/(44+x)]

(x -20) = (44+x) ×  0

x - 20 = 0

x = 20

Hence, the missing frequency is 20 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The missing frequency is 20.

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 18.

$\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6}Class & x_i & f_i & d_i & u_i & f_{i}u_i\\ \cline{1-6}11-13 & 12 & 7 & -6 & -3 & -21\\ \cline{1-6}13-15 & 14 & 6 & -4 & -2 & -12\\ \cline{1-6}15-17 & 16 & 9 & -2 & -1 & -9\\ \cline{1-6}17-19 & 18 & 13 & 0 & 0 & 0\\ \cline{1-6}19-21 & 20 & x & 2 & 1 & x\\ \cline{1-6}21-23 & 22 & 5 & 4 & 2 & 10\\ \cline{1-6}23-25 & 24 & 4 & 6 & 3 & 12\\ \cline{1-6} & & \Sigma f_{i}=44+x & & & \Sigma f_{i}u_{i}=x-20\\ \cline{1-6}\end{tabular}$

Since, mean -

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

$\implies 18=18+2\times\frac{(x-20)}{(44+x)}$

$\implies 18-18=2\times\frac{(x-20)}{(44+x)}$

$\implies (x-20)=(44+x)\times 0$

$\implies x-20=0$

$\implies x=20$