Compute the mode of the following data:
Class interval | 1 - 5 | 6 - 10 | 11 - 15 | 16 - 20 | 21 - 25 | 26 - 30 | 31 - 35 | 36 - 40 | 41 - 45 | 46 - 50 |
Frequency | 3 | 8 | 13 | 18 | 28 | 20 | 13 | 8 | 6 | 4 |
Since, the given data is in inclusive series, it needs to get converted in exclusive series.
CLASS INTERVAL | 0.5 - 5.5 | 5.5 - 10.5 | 10.5 - 15.5 | 15.5 - 20.5 | 20.5 - 25.5 | 25.5 - 30.5 | 30.5 - 35.5 | 35.5 - 40.5 | 40.5 - 45.5 | 45.5 - 50.5 |
FREQUENCY | 3 | 8 | 13 | 18 | 28 | 20 | 13 | 8 | 6 | 4 |
Here, the maximum class frequency is 28.
The class corresponding to this frequency is the modal class. ⇒ modal class = 15.5 - 20.5
∴ lower limit of the modal class (l) = 15.5
Modal class size (h) = 5
Frequency of the modal class (f1) = 28
Frequency of class preceding the modal class (f0) = 18
Frequency of class succeeding the modal (f2) = 20
Mode is given by,
⇒ 
⇒ 
⇒ Mode = 15.5 + 2.78 = 23.28
Hence, the mode is 23.28.