Question

Find the mode for the following frequency distribution.

Class	1 – 10	11 – 20	21 – 30	31 – 40	41 – 50
Frequency	2	3	5	7	1

Use formula: Mode = `L = (f_0 - f_1)/(2f_0 - f_1 - f_2) xx h`

Answer 1

Step 1: Convert discontinuous classes to continuous classes

Since the class intervals are discontinuous (1 – 10, 11 – 20, etc.), we must make them continuous by subtracting 0.5 from the lower limits and adding 0.5 to the upper limits.

Original Class	Continuous Class	Frequency
1 – 10	0.5 – 10.5	2
11 – 20	10.5 – 20.5	3
21 – 30	20.5 – 30.5	5
31 – 40	30.5 – 40.5	7
41 – 50	40.5 – 50.5	1

Step 2: Identify the variables for the formula

From the table, the highest frequency is 7, which makes 30.5 – 40.5 our modal class.

Using the notation provided in your formula:

L (Lower boundary of the modal class) = 30.5 

f₀ (Frequency of the modal class) = 7

f₁ (Frequency of the preceding class) = 5

f₂ (Frequency of the succeeding class) = 1

h (Class width) = 40.5 – 30.5 = 10

Step 3: Calculate the mode

Substitute these values into the standard mode formula:

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

Mode = `30.5 + ((7 - 5)/(2(7) - 5 - 1)) xx 10`

Mode = `30.5 + (2/(14 - 6)) xx 10`

Mode = `30.5 + (2/8) xx 10`

Mode = 30.5 + 0.25 × 10

Mode = 30.5 + 2.5

Mode = 33