Question

53. Find the missing frequencies ſi and $2 in the following frequency distribution. if
n = 100 and median is 32:
poin
Class
0-10
10-20 20-30 30-40 40-50 50-60
Total
Frequency (1)
d th
10
fi
25
30
f2
10
100​

Answer 1

Step-by-step explanation:

Given:-

Classes :

0-10,10-20,20-30,30-40,40-50,50-60

Frequencies:-

10,f1,25,30,f2,10

Median = 32

Number of observations = 100

To find:-

Find the missing numbers f1 and f2

Solution:-

Refer the above attachment

Number of observations = 100

=>75+f1+f2 = 100

=>f1+f2 = 100-75

f1 + f2 = 25 --------(1)

Median = 32

So it lies in the class 30-40

So Median class = 30-40

Lower limit of the median class (l)=30

Frequency of the median class (f)=30

Cumulative frequency of the class preceding the class = (cf) = 35+f1

Length of the class (h)=10

n/2 = 100/2 = 50

We know that

Median = (l)+[(n/2)-cf)/f]×h

=>32 = 30 +[{50-(35+f1)}/30]×10

=>32 = 30 +[50-35-f1)/3]

=>32-30 = (50-35-f1)/3

=>2 = (15-f1)/3

=>2 ×3 = 15-f1

=>6 = 15-f1

=>f1 = 15-6

=>f1 =9

From (1)

9+f2 = 25

=>f2 = 25-9

=>f2 = 16

Answer:-

The missing numbers f1 = 9 and f2 = 16

Used formula:-

• Median = (l)+[(n/2)-cf)/f]×h
• l= lower limit of the median class
• n= No.of observations
• cf= Cumulative frequency of the class preceding the median class
• f = frequency of the median class
• h=height of the class