The agewise participation of students in the Annual Function of a school is shown in the following distribution.
Age (in years) | 5 - 7 | 7 - 9 | 9 - 11 | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 |
Number of students | x | 15 | 18 | 30 | 50 | 48 | X |
Find the missing frequencies when the Sum of frequencies is 181. Also, find the mode of the data.
To find frequencies, we have Sum of frequencies that is, 181.
Using Sum of frequencies = 181,
x + 15 + 18 + 30 + 50 + 48 + x = 181
⇒ 2x + 161 = 181
⇒ 2x = 181 – 161 = 20
⇒ x = 10
Thus we have,
Age (in years) | 5 - 7 | 7 - 9 | 9 - 11 | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 |
Number of students | 10 | 15 | 18 | 30 | 50 | 48 | 10 |
Here, the maximum class frequency is 50.
The class corresponding to this frequency is the modal class. ⇒ modal class = 13 - 15
∴ lower limit of the modal class (l) = 13
Modal class size (h) = 2
Frequency of the modal class (f1) = 50
Frequency of class preceding the modal class (f0) = 30
Frequency of class succeeding the modal (f2) = 48
Mode is given by,
⇒
⇒
⇒ Mode = 13 + 1.82 = 14.82
Hence, the mode is 14.82.