Question

In a school the weekly pocket money of 50 students is as follows. Find mode of pocket money.

Pocket money (in ₹)	40 – 50	50 – 60	60 – 70	70 – 80	80 – 90	90 – 100
No. of students	2	8	12	14	8	6

Answer 1

1. Identify the modal class

The modal class is the class interval with the highest frequency.

The maximum frequency is 14, which belongs to the class interval 70 – 80.

Therefore, the modal class = 70 – 80.

2. Extract the Values

`l` (lower limit of the modal class) = 70

f₁ (frequency of the modal class) = 14

f₀ (frequency of the class preceding the modal class) = 12

f₂ (frequency of the class succeeding the modal class) = 8 

h (class size or width) = 80 – 70 = 10

3. Substitute values into the formula

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

Mode = `70 + ((14 - 12)/(2(14) - 12 - 8)) xx 10`

Mode = `70 + (2/(28 - 20)) xx 10`

Mode = `70 + (2/8) xx 10`

Mode = 70 + 0.25 × 10

Mode = 70 + 2.5

Mode = 72.5