(Q10) 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.

Solution :

Maximum number of patients joined in the age group 35-45.

∴ Modal class is 35-45.

Lower limit of the Modal Class 'l' = 35

Class size h = 10

Frequency of modal class, f1 = 23

Frequency of the class preceding the modal class f0 = 21

Frequency of the class succeeding the modal class f2 = 14

Age Number of Patients(fi) xi fixi
5-15 6 10
15-25 11 20
25-35 21 30
35-45 23 40
45-55 14 50
55-65 5 60
- ∑fi = 80 - ∑fixi =
Mode = l +
f1 - f0
2f1 - f0 - f2
 × h
Mode = 35 +
-
2 × - -
× = 35 +
× = .8 years
Mean x =
∑fixi
∑fi
 =
80
 = .37 years

Mode age is .8 years, Mean age = .37 years.

Maximum number of patients admitted in the hospital are of the age 36.8 years, while on an average the age of patients admitted to the hospital is 35.37 years. Mode is less than the Mean.