Question

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observation in the data:
Class interval
0−100
100−200
200−300
300−400
400−500
Frequency
2
5
f1
12
17
Class interval
500−600
600−700
700−800
800−900
900−1000
Frequency
20
f2
9
7
4

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is in the attachment.  

Given : Median = 525 , which  belongs to the class 500 - 600 . So the Median class is 500 - 600  

Given : n(Σfi) = 100  

Here, n = 100

n/2 = 50

From the table , l = 500, f = 20, cf = (36 + f1) , h = 100

MEDIAN = l + [(n/2 - cf )/f ] ×h

525 = 500 +[50- (36+f1)/20] ×100

525 - 500 = [(50 - 36 - f1)/20] × 100

25 = [ (14 - f1)/20] × 100

25 × 20 = (14 - f1) × 100

500 = 1400 - 100f1

100 f1 = 1400 - 500

100f1 = 900

f1 = 900/100

f1 = 9  

Given : Σfi = 100  

76 + f1 + f2 = 100

f1 + f2 = 100 - 76

f1 + f2 = 24

f2 = 24 - f1

f2 = 24 - 9       [f1 = 9]

f2 = 15

Hence, the missing frequencies be  f1 = 9 and f2 = 15.

★★ 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…