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  • 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)

best_answer

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.

Posted by

HARSH KANKARIA

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