An incomplete distribution is given below :
Variable:
10−20
20−30
30−40
40−50
50−60
60−70
70−80
Frequency:
12
30
−
65
−
25
18
You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
Answers
SOLUTION :
CUMULATIVE FREQUENCY TABLE are in the attachment.
Let the missing frequencies be x and y.
Given : n(Σfi) = 230 , Median = 46
From the table, Σfi = 150 + x + y ,
Here, n = 230
n/2 = 115
Given , Median = 46, which belongs to the class 40 - 50 . So the Median class is 40 - 50 .
Here, l = 40 , f = 65, c.f = (42 + x) , h = 10
MEDIAN = l + [(n/2 - cf )/f ] ×h
46 = 40 + [(115 - (42+x))/65] × 10
46 - 40 = [(115 - (42+x))/65] × 10
6 = [(115 - 42 - x)/65] × 10
6 =[ (73 - x)/65]×10
(6× 65)/10 = 73 - x
(3 × 65)/5 = 73 - x
3 × 13 = 73 - x
39 = 73 - x
x = 73 - 39
x = 34
Σfi = 150 + x + y
230 = 150 + 34 + y [Σfi = 230 , x = 34]
230 = 184 + y
y = 230 - 184
y = 46
Hence, the missing frequencies be x = 34 and y = 76 .
(ii) MEAN:
MEAN = A + h ×(Σfiui /Σfi)
From the table, Σfiui = 20 , Σfi = 230
Let the assumed mean, A = 45, h = 10
Mean = 45 + 10(20/230)
= 45 + 20/23
= 45 + 0.87
= 45.87
Hence, the Mean is 45.87 .
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Step-by-step explanation:
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