Question

The following table shows the ages of the patients admitted in a hospital during a year:
Ages (in years):
5-15
15-25
25-35
35-45
45-55
55-65
No of students:
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

SOLUTION :  

Mode = l + (f1-f0/2f1-f0-f2) ×h

l = lower limit of the modal class

h = size of the class intervals

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeed in the modal class.

FREQUENCY DISTRIBUTION TABLE is in the attachment  

Here the maximum frequency is 23, and the class corresponding to this frequency is 35 – 45. So the modal class is 35 - 45 .

Therefore,l = 35 , h = 45 – 35 = 10,  f1 = 23, , f0 = 21, f2 = 14

Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h

= 35 + [(23 - 21)/(2×23- 21 – 14) ]×10

= 35 +[(2 × 10)/(46 - 35)]

= 35 + [20/11]

= 35 + 1.81

= 36.81

Hence, the MODE ages of a patient is 36.81 years  

MEAN :  

From the table : Σf = 80 , Σfx = 2830

Mean = Σfx /Σf

Mean = 2830/80 = 283/8 = 35.37 years  

Hence, the Mean ages of a patient is 35.37 years  

Hence, the mean age of the patient is less than the modal age of patients.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Refer to the attachment please.