Question

1.
The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years)
5-15
15-25
25-35
35-45
45-55
55-65
Number of patients
6
11
21
23
14
5
Find the mode and the mean of the data given above. Compare and interpret the two
measures of central tendency.​

Answer 1

Answer:

Mode: The class which have highest frequency.

In this case, class interval 35−45 is the modal class.

Now,

Lower limit of modal class, l=35,h=10,f

1

,=23,f

0

=21,f

2

=14

We know that,

Mode =l+(

2f

1

−f

0

−f

2

f

1

−f

0

)×h

=35+(

2(23)−21−14

23−21

)×10

=35+

11

2

×10

=35+1.818

Mode =36.8

Lets take assumed mean, A as 30

Class interval =10

∴u

i

=

h

x

i

−A

=

10

x

i

−30

x

ˉ

=A+h

∑f

i

∑f

i

u

i

=30+10×

80

43

=30+5.375

=35.375

≈35.37

Hence, Mode =36.8 years, Mean =35.37 years.

Maximum number of patients admitted in the hospital are of age group 36.8 years, while on an average the age of a patient admitted to the hospital is 35.37 years.

solution