Question

Marks of 60 students in a class are tabulated below. For finding mode the Lower limit of modal class (L) = --------

Marks	10 – 19	20 – 29	30 – 39	40 – 49	50 – 59	60 – 69
Number of students	3	8	16	12	10	8

Answer 1

1. Identify the modal class

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

The maximum frequency is 16.

This corresponds to the class interval 30 – 39.

2. Convert to continuous class intervals

To find the exact value of L for the standard mode formula, the data must be continuous.

Adjustment factor = `("Lower limit of next class" - "Upper limit of current class")/2`

= `(20 - 19)/2`

= 0.5

Subtract 0.5 from each lower limit and add 0.5 to each upper limit:

Marks (Original)	Marks (Continuous)	Number of students (Frequency)
10 – 19	9.5 – 19.5	3
20 – 29	19.5 – 29.5	8
30 – 39	29.5 – 39.5	16 (Highest)
40 – 49	39.5 – 49.5	12
50 – 59	49.5 – 59.5	10
60 – 69	59.5 – 69.5	8

3. Determine the Lower Limit (L)

In the continuous form, the modal class is 29.5 – 39.5.

Therefore, the precise lower boundary (L) used in the mode formula is 29.5.