Question

daily wages of 100 labourers is given in following frequency distribution find the mean of data by step division method​

Answer 1

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Secondary School Math 15 points

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.

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Answers

nikitasingh79

nikitasingh79 Genius

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 .

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Answer 2

Answer:

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 .

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