Economy, asked by sukhBularia, 11 months ago

calculate arithmetic mean from data using short cut and step deviation method

Answers

Answered by rajputayush30
1

Answer:

Step Deviation : Sometimes, during the application of the short-cut method for finding the mean, the deviation d, are divisible by a common number ‘h’ .In this case the di = xi – A is reduced to a great extent as di becomes di / h. So the formula of mean by this is :

Where ui = ( xi – A) / h ; h = class width and N = Σ fi

Finding mean by using this formula is known as the Step Deviation Method.

Some solved examples

1) Apply Step - Deviation method to find arithmetic mean of the following frequency distribution.

variate

5

10

15

20

25

30

Frequency

20

43

75

67

72

45

Solution:

Let the assumed mean be A = 20 and h = 5.

Variate (xi)

Frequency (fi)

Deviation= di = xi - 20

ui = (xi - 20 )/ 5

fi ui

5

20

-15

-3

-60

10

43

-10

-2

-86

15

75

-5

-1

-75

20

67

0

0

0

25

72

5

1

72

30

45

10

2

90

N = Σ fi = 322

-59

N = 322, A = 20 , h = 5 and Σ fi ui = - 59

⇒ Mean = 20 + 5 ( - 59 / 322)

⇒ Mean = 20 – 0.91

∴ Mean = 19.09

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