Question

An incomplete distribution is given as follows:
Variable:
0−10
10−20
20−30
30−40
40−50
50 − 60
60 − 70
Frequency:
10
20
?
40
?
25
15
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Answer 1

SOLUTION :  

Let the missing frequency of the class 20 - 30 be f1 and that of class 40 - 50 be f2.

Given : n(Σfi) = 170 , Median = 35

From the table, Σfi = 10 + 20 + f1 + 40 + f2 + 25 + 15  

170 = 110 + f1 + f2

f1 + f2 = 170 - 110  

f1 + f2 = 60 …………….(1)

Here, n = 170

n/2 = 85

Given , Median =  35, which  belongs to the class 30 - 40 . So the Median class is 30 - 40 .

Here, l = 30 , f = 40, c.f = (30 + f1) ,   h = 10

MEDIAN = l + [(n/2 - cf )/f ] ×h

35 = 30 + [(85 - (30 + f1 ))/40] × 10

35 - 30 = [(85 - 30 - f1 ))/40] × 10

5 = [(55 - f1)/40] × 10

5 = [(55 - f1)/4

5 × 4 = 55 - f1

20 = 55 - f1

f1 = 55 - 20

f1 = 35  

Put the value of f1 in eq 1

f1 + f2 = 60

35 + f2 = 60

f2 = 60 - 35

f2 = 25

Hence, the missing frequencies be  f1 = 35 and f2 = 25.

★★ MEDIAN = l + [(n/2 - cf )/f ] ×h

Where,

l = lower limit of the median class

n = number of observations  

cf = cumulative frequency  of class interval preceding the  median class

f = frequency  of median class

h = class  size

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :

Please Refer the given attachment for the answer.

Thus,

$\sf{f_1 = 35}$

$\sf{f_2 = 25}$

Hope it helps.

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