Calculate mode from the given data.Class Interval 0-5 5-10 10-15 15-20 20-25 Number of states 15 10 6 7 2
3.75
The modal class is the class with the highest frequency. Here the highest frequency is 15, so the modal class is 0-5.
Mode \(= L + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h\), where \(L\) is the lower boundary of the modal class, \(f_1\) the modal-class frequency, \(f_0\) the frequency of the preceding class, \(f_2\) the frequency of the following class, and \(h\) the class width.
Here \(L = 0\), \(f_1 = 15\), \(f_0 = 0\) (no class before 0-5), \(f_2 = 10\), and \(h = 5\).
Mode \(= 0 + \dfrac{15 - 0}{2(15) - 0 - 10} \times 5 = \dfrac{15}{20} \times 5 = 3.75\).
Hence, the mode of the given distribution is 3.75.
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