Q&A - Ask Doubts and Get Answers
Q

The following table shows the ages of the patients admitted in a hospital during a year:

1.   The following table shows the ages of the patients admitted in a hospital during a year:

       2.1

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answers (1)
Views

The class having maximum frequency is the modal class.

The maximum frequency is 23 and hence the modal class = 35-45

Lower limit (l) of modal class = 35, class size (h) = 10 

Frequency ( f_1 ) of the modal class = 23, frequency ( f_0 ) of class preceding the modal class = 21, frequency ( f_2 ) of class succeeding the modal class = 14.

Mode = l + \left(\frac{f_1-f_0}{2f_1 - f_0 - f_2} \right).h

\\ = 35 + \left(\frac{23-21}{2(23)-21-14} \right).10 \\ \\ = 35 + \frac{2}{11}.10

= 36.8

Now,

Age

 

Number of

patients f_i

Class mark

x_i

f_ix_i
5-15 6 10 60
15-25 11 20 220
25-35 21 30 630
35-45 23 40 920
45-55 14 50 700
55-65 5 60 300
 

\sum f_i 

=80

 

\sum f_ix_i

=2830

Mean, 

\overline x = \frac{\sum f_ix_i}{\sum f_i}
= \frac{2830}{80} = 35.37
The maximum number of patients are in the age group of 36.8, whereas the average age of all the patients is 35.37.

Exams
Articles
Questions