Question

The following table shows the age distribution of cases of certain disease admitted

during a year in particular hospital.


Age (in years) No. of cases

5 – 14 6

15 – 24 11

25 – 34 21

35 – 44 23

45 – 54 14

55 – 64 5

TOTAL 80

Draw a histogram and hence find the mode from the graph.

Answer 1

Step-by-step explanation:

$Here class intervals are not inclusive form. So, we first convert them in inclusive from by subtracting h/2 from the lower limit and adding h/2 to the upper limit of each class, where h is the difference between the lower limit of a class and the upper limit of the preceding class. The given frequency distribution in inclusive form is as follows.</p><p></p><p>Age ( in years)4.5-14.5 14.5-24.5 24.5-34.5 34.5-44.5 44.5-54.5 54.5-64.5No. of cases:6112123145 We observe that the class 34.5−44.5 has the maximum frequency. So, it is the modal class such that,</p><p>l=34.5,h=10,f=23,f1=21,andf2=14</p><p>∴Mode=l+2f−f1−f2f−f1×h</p><p>⇒Mode=34.5+46−21−1423−21×10</p><p>⇒Mode=34.5+111×10</p><p>⇒Mode=36.31$