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

## 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.