The following table shows the ages of the patients admitted in a hospital. Find the mode of the given data.

Question :

Age (in years)5 – 1515 – 2525 – 3535 – 4545 – 5555 – 65
No. of cases6112123145

Solution :

The class (35 – 45) has maximum frequency, i.e. 23 therefore this is the modal class.

Lower limit of the modal class = l = 35

Width of Class – interval = h = 10

Frequency of the modal class = \(f_k\) = 23

Frequency of the class preceding the modal class = \(f_{k-1}\) = 21

Frequency of the class succeeding the modal class = \(f_{k+1}\) = 14

Mode = l + h(\(f_k – f_{k-1}\over 2f_k – f_{k-1} – f_{k+1}\)) = 35 + 10(\(23 – 21\over 46 – 35\))

Mode = 35 + \(20\over 11\) = 35 + 1.8181 = 36.818

Hence, the average age for which maximum cases occurred is 36.818.

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