Question

Consider the following distribution of daily wages of 50 worker of a factory. Daily wages (in Rs) 100­ − 120 120­ − 140 140 −1 60 160 − 180 180 − 200 Number of workers 12 14 8 6 10 Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer 1

Answer:

The mean daily wage of the workers is ₹ 145.20 .

Step-by-step explanation:

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

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfiui = -12 , Σfi = 50

Let the assumed mean, A = 150, h = 20

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 150 + 20(-12/50)

= 150 - 24/5

= 150 - 4.8

= 145.2  

Hence, the mean daily wage of the workers is ₹ 145.20 .

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

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:

$\begin{tabular}{|l|l|l|l|} \cline{1-4} Class & Freq & (x_i) & x_i f_i \\ \cline{1-4} 100-120& 12 & 110 & 1320 \\ \cline{1-4} 120-140 & 14 & 130 & 1820 \\ \cline{1-4} 140-160 & 8 & 150 & 1200 \\ \cline{1-4} 160-180 & 6 & 170 & 1020 \\ \cline{1-4} 180-200 & 10 & 190 & 1900 \\\cline{1-4} Total & 50 & & 7260 \\ \cline{1-4} \end{tabular}$

$class \: mark : x_i = \frac{upper \: class \: limit + lower \: class \: limit}{2} \\ \\ xi = \frac{100 + 120}{2} = \frac{220}{2} = 110$
Direct Mean Method:

$\bar{x} = \frac{ \Sigma \: x_i \: f_i}{\Sigma \: f_i} \\ \\ \bar{x} = \frac{7260}{50} \\ \\ \bar{x} = 145.20 \: \: Rs$
Hope you like the simplest way of calculating mean.