If the median of the following data is 32.5

Asked by admin @ 16/08/2021 in Math viewed by 327 People

If the median of the following data is 32.5, find the missing frequencies.

Class interval:
0−10
10−20
20−30
30−40
40−50
50−60
60−70
Total
Frequency:
f1
5
9
12
f2
3
2
4

Answered by admin @ 16/08/2021

SOLUTION :

CUMULATIVE FREQUENCY TABLE is in the attachment.

Given : Median = 32.5 , which belongs to the class 30 - 40 . So the Median class is 30 - 40

Given : n(Σfi) = 40

Here, n = 40

n/2 = 20

From the table , l = 30, f = 12, cf = (14 + f1) , h = 10

MEDIAN = l + [(n/2 - cf )/f ] ×h

32.5 = 30 +[ 20- (14+f1)/12] ×10

32.5 - 30 = [(20- 14 + f1)/12] ×10

2.5 =[ (6 - f1)/12 ]×10

2.5 × 12 = 60 -10 f1

30 - 60= -10f1

-30 = -10f1

f1 = 30/10 = 3

f1 = 3

Given : Σfi = 40

31 + f1 + f2 = 40 [from the table]

f1 + f2 = 40 - 31

3 + f2 = 9 [f1 = 3]

f2 = 9 - 3

f2 = 6

Hence, the missing frequencies be f1 = 3 and f2 = 6

★★ 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

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