Question :
| Age (in years) | 5 – 15 | 15 – 25 | 25 – 35 | 35 – 45 | 45 – 55 | 55 – 65 |
| No. of cases | 6 | 11 | 21 | 23 | 14 | 5 |
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.
