Question

1.
The following table shows the age distribution of cases of a certain disease admitted during a year in a
particular hospital:
5-14
25-34
35-44
55-64
15-24
45-54
Age (in years)
11
21
6
23
14
Number of cases
5
Find the average age for which maximum cases occurred.​

Answer 1

Here class intervals are not inclusive form. So, we first convert them in inclusive from by subtracting h/2 from the lower limit and adding h/2 to the upper limit of each class, where h is the difference between the lower limit of a class and the upper limit of the preceding class. The given frequency distribution in inclusive form is as follows.

Age ( in years) 4.5-14.5 14.5-24.5 24.5-34.5 34.5-44.5 44.5-54.5 54.5-64.5

No. of cases: 6 11 21 23 14 5

We observe that the class 34.5−44.5 has the maximum frequency. So, it is the modal class such that,

l=34.5,h=10,f=23,f

1

=21,andf

2

=14

∴Mode=l+

2f−f

1

−f

2

f−f

1

×h

⇒Mode=34.5+

46−21−14

23−21

×10

⇒Mode=34.5+

11

1

×10

⇒Mode=36.31

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