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.

Answer 1

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.