Now,
F2= 100 (Total Frquency) -
(14+f1+27+15)
OR
F2 = 44-f1
Calculation of Median

Expenditure
No. of Families
Cumulative Frequency
0-20
14
14
20-40
f1
14+f1
40-60
27
41+f1
60-80
f2
85+f1-f1=85
80-100
15
100
Median is given in this problem as 50
Middle item of the series is also 100/2 is 50
Which means it lies in the class-interval 40-60
Now, Formula for Median is
M
=
l
1
+
l
2
−
l
1
f
1
(
m
−
c
)
50
=
40
+
60
−
40
27
[
50
−
(
14
+
f
1
)
]
50
=
40
+
20
27
[
36
+
f
1
]
F1 = 22.5
Since the frequency in this position cannot be in fraction so f1 would be taken as 23.
F2=44-f1 or 44-23 or 21
Thus the missing values in the question are 23 and 21.
Practice Example 32
An incomplete distribution is given below
Variable
Frequency
10-20
12
20-30
30
30-40
?
40-50
65
50-60
?

60-70
25
70-80
18
Total Frequency
229
(Answer: missing frequencies are 34 and 45, mean = 45.83)
Calculation of Median in Open End Series
Example 33
You are given below a certain statistical distribution
Value
Frequency
Less than 100
40
100-200
89
200-300
148
300-400
64
400 and above
39
Calculate the most suitable average giving reasons for your choice.
(Answer: Median = 241.2)
[Hint: since the series has open ends, we cannot calculate mean. Median would be the most suitable
average in such a case.]
Merits of Median
1.
It is easily understood
2.
It is not affected by extreme values
3.
It can be located graphically
4.
It is the best measure for qualitative data such as beauty, intelligence, honesty etc.
5.
It can be easily located even if the class-intervals in the series are unequal
6.
It can be determined even by inspection in many cases
Drawbacks of Median
1.
It is not subject to algebraic treatments
2.
It cannot represent the irregular distribution series
3.
It is positional average and is based on the idle item
4.
It does not have sampling stability
5.
It is an estimate in case of a series containing even number of items
6.
It does not take into account the values of all the items in the series
7.
It is not suitable in those cases where due importance and weight should be given to extreme
values