Question

Find the modal height of the following distribution by drawing a histogram:

Height (in cm)	140 – 150	150 – 160	160 – 170	170 – 180	180 – 190
Frequency	7	6	4	10	2

Answer 1

Calculation Steps 

1. Identify the modal class: Find the class interval with the highest frequency. Here, the frequency 10 is the maximum, so the modal class is 170 – 180.

2. Determine graphical parameters: To find the mode from a histogram, draw two lines intersecting inside the modal bar:

1. From the top-left corner of the modal bar to the top-left corner of the next bar.
2. From the top-right corner of the modal bar to the top-right corner of the previous bar.
3. The x-coordinate of the intersection point is the mode. 

3. Apply the mode formula: For a more precise value, use the grouped data formula:

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

Where:

1. L (Lower limit of modal class) = 170
2. f₁ (Frequency of modal class) = 10
3. f₀ (Frequency of preceding class) = 4
4. f₂ (Frequency of succeeding class) = 2
5. h (Class width) = 10

4. Compute the final value:

Mode = `170 + ((10 - 4)/(2(10) - 4 - 2)) xx 10`

Mode = `170 + (6/14) xx 10`

= 170 + 4.2857

= 174.3