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.

Question

Philoid · Accepted Answer

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.

The agewise participation of students in the Annual Function of a school is shown in the following distribution.Age (in years)5 - 77 - 99 - 1111 - 1313 - 1515 - 1717 - 19Number of studentsx1518305048XFind the missing frequencies when the Sum of frequencies is 181. Also, find the mode of the data.