Calculating Mean using Step Deviation Method


 
 
Concept Explanation
 

Calculating Mean using Step Deviation Method

Calculating Mean Using Step Deviation Method:

Sometimes, while calculating mean using assumed mean method we find that the deviation d, are divisible by a common number . Let us assume the common factor as h. The deviation is then divided by h and the resultant number is denoted by u. In this way the value of d is reduced to a great  extent and hence the calculations become more simple. The method is called the step-deviation method, and we can express it

Mean (bar{x}) = a+ h timesleft (frac{ sum {f_{i}u_{i}}} {sum{f_{i}}} right ) 

Where , a = Assumed mean ,  u_{i}=frac{x_{i}-a}{h} ,

h=class size

Illustration:   The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by step deviation method.

Percentage of female teacher 15-25 25-35 35-45 45-55 55-65 65-75 75-85
number of status/U.T 6 11 7 4 4 2 1

Solution : Let us find the class mark, xi, of each class, and put them in a column 

Here we take  a = 50,

h = 10,

d_{i} = x_{i} -50

u_{i} = frac{d_{i}}{10}

Percentage of female teachers Numbers of states or U.T.(f_{i})

Class Mark

x_{i}

d_{i}=x_{i}-50 u_{i}=frac{x_{i}-50}{10} large f_{i}u_{i}

15-25

25-35

35-45

45-55

55-65

65-75

75-85

6

11

7

4

4

2

1

20

30

40

50

60

70

80

-30

-20

-10

0

10

20

30

-3

-2

-1

0

1

2

3

-18

-22

-7

0

4

4

3

Total 35       -36

Using the step-deviation method,

   bar{x}=a+ htimes left ( frac{sum f_i u_i}{sum f_i} right )=50+10times left(frac{-36}{35} right) =50-10.29 = 39.71

Therefore, the mean percentage of female in the primary schools of rural areas is 39.71.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

What will be the value of f_iu_i while finding mean using step - deviation method for the class interval 0 -20 following distribution :

Marks No. of students
0 - 20 14
20 - 40 12
40 - 60 30
60 - 80 16
80 - 100 18
Right Option : D
View Explanation
Explanation
Question : 2

What will be the value of u_i while finding mean using step - deviation method for the class interval 0 -20 following distribution :

Marks No. of students
0 - 20 14
20 - 40 12
40 - 60 30
60 - 80 16
80 - 100 18
Right Option : D
View Explanation
Explanation
Question : 3

What will be the value of h while finding mean using step - deviation method for the following distribution :

Marks No. of students
15 - 20 4
20 - 25 2
25 - 30 3
30 - 35 6
35 - 40 5

 

Right Option : B
View Explanation
Explanation
 
 
 


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