Question

Consider the following distribution of daily wages of workers of a factory
Daily wages (in Rs) 100-120 120-140 140-160 160-180 180-200
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

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

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 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

145.2

Step-by-step explanation:

Refer to the attachment for table.

Since the Summation of Frequency times Class mark has hugh values, we use Step Deviation method which simplifies the job.

Here, Class Width or Height is 20.

Formula for calculating Mean using Step Deviation Method:

$\bar{x} = A \: + \dfrac{ \sum fu}{ \sum f} \times h$

Substituting in the formula, we get,

⇒ Mean = 150 + ( -12 / 50 ) × 20

⇒ Mean = 150 + ( -240 / 50 )

⇒ Mean = 150 + ( -4.8 )

⇒ Mean = 150 - 4.8 = 145.2

Hence the mean of the given distribution is 145.2