Question

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

Answer 1

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

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

Step-by-step explanation: