1. 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
35-4545-55 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.
Answers
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.
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