14.3(3)A life insurance agent found the following data for distribution of age
of 100 policy holders. Calculate median age, if policies are given only to the
persons having age 18 years onwards but less than 60 years.
Age (in years) | Below 20 | Below 25 | Below 30 | Below 35 | Below 40 | Below 45 | Below 50 | Below 55 | Below 60 |
Frequency | 2 | 6 | 24 | 45 | 78 | 89 | 92 | 98 | 100 |
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Age (in years)
Below 20
Below 25
Below 30
Below 35
Below 40
Below 45
Below 50
Below 55
Below 60
Cuml. frequency
2
6
24
45
78
89
92
98
100
Class
15 - 20
20 - 25
25 - 30
30 - 35
35 - 40
40 - 45
45 - 50
50 - 55
55 - 60
Frequency
100 – 98 = 2
98 – 92 = 6
92 – 89 = 3
89 – 78 = 11
78 – 45 = 33
45 – 24 = 21
24 – 6 = 18
6 – 2 = 4
2
f
Exercise 14.3 – Q.3
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n
2
Here
=
100
2
= 50
Median class is 35 - 40
l = 35,
h = 5,
f = 33,
c.f. = 45,
Class
frequency
Cum. frequency
15 - 20
20 - 25
25 - 30
30 - 35
35 - 40
40 - 45
45 - 50
50 - 55
55 - 60
100 – 98 = 2
98 – 92 = 6
92 – 89 = 3
89 – 78 = 11
78 – 45 = 33
45 – 24 = 21
24 – 6 = 18
6 – 2 = 4
2
2
6
24
45
78
89
92
98
100
Median
l +
n
2
-
c. f .
f
×
h
=
35
+
50
-
45
33
×
5
=
35
+
25
33
=
35
+
0.76
Median
=
35.76
f
c.f
which line in the class 35 - 40
Which c.f just greater than or equal to ?
50
Cumulative frequency of the class preceeding the median class (c.f.)
=
0.76
Exercise 14.3 – Q.3