A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year
Solution:
Here, class width is not the same. There is no requirement of adjusting the frequencies according to class intervals. The given frequency table is of less than type represented with upper class limits.
Median Class is the class having Cumulative frequency(cf) just greater than n/2
Median = l + [(n/2 - cf)/f] × h
Class size, h
Number of observations, n
Lower limit of median class, l
Frequency of median class, f
Cumulative frequency of class preceding median class, cf
Class intervals with their respective cumulative frequency can be defined as below
From the table, it can be observed that
n = 100 ⇒ n/2 = 50
Cumulative frequency (cf) just greater than 50 is 78, belonging to class-interval 35 − 40
Therefore, median class = 35 - 40
Class size, h = 5
Lower limit of median class, l = 35
Frequency of median class, f = 33
Cumulative frequency of class preceding median class, cf = 45
Median = l + [(n/2 - cf)/f] × h
= 35 + [(50 - 45)/33] × 5
= 35 + 25/33
= 35 + 0.76
= 35.76
Therefore, median age is 35.76 years
☛ Check: NCERT Solutions for Class 10 Maths Chapter 14
Video Solution:
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 Question 3
Summary:
A life insurance agent found the following data for distribution of ages of 100 policy holders. If policies are given only to persons having age 18 years onwards but less than 60 year, the median age is 35.76 years.
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