Find the mean of each of the following frequency distributions :
Class interval:
50-70
70-90
90-110
110-130
130-150
150-170
Frequency:
18
12
13
27
8
22
Answers
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
[‘Σ’ Sigma means ‘summation’ ]
FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT
From the table : Σfiui = 61 , Σfi = 100
Let the assumed mean, A = 100, h = 20
MEAN = A + h ×(Σfiui /Σfi)
MEAN = 100 + 20 (61/100)
= 100 + 61/5
= 100 + 12.20
Mean = 112.20
Hence, the mean is 112.20
HOPE THIS ANSWER WILL HELP YOU….
_____Here's your Answer _______
A = 100.
h = 20.
fiui = 61
fi = 100
Now,
Mean = A + h× ( fiui / fi)
=> 100 + 20 × ( 61 / 100)
=> 100 + 61 / 5
=> (500 + 61 ) / 5
=> 561 / 5
=> 112.2
Therefore ,
Mean is 112.2
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