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Question
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.
Solution
It is given that the sum of frequencies is 181.
∴ x + 15 + 18 + 30 + 50 + 48 + x = 181
⇒ 2x + 161 = 181
⇒ 2x = 181 – 161
⇒ 2x = 20
⇒ x = 10
Thus, x = 10
Here, the maximum class frequency is 50, and the class corresponding to this frequency is 13 – 15. So, the modal class is 13 – 15.
Now,
Modal class = 13 – 15, lower limit (l) of modal class = 13, class size (h) = 2,
frequency `(f_1)` of the modal class = 50,
frequency `(f_0)` of class preceding the modal class = 30,
frequency `(f_2) `of class succeeding the modal class = 48
Now, let us substitute these values in the formula:
Mode =` l + ((f_1− f_0)/(2f_1− f_0− f_2)) × h`
`= 13 + ((50−30)/(100−30−48)) × 2`
`= 13 + (20/22) × 2`
= 13 + 1.82
= 14.81
Hence, the mode is 14.81.
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