Question

Find Mode

• A. \(34.12\)
• B. \(33.75\)
• C. \(31.67\)
• D. \(32.14\)

Hint:

Always identify the class having maximum frequency first. That class is called the modal class and is used in the grouped-data mode formula.

Answer 1

The Correct Option is D

Concept: For grouped data, Mode is calculated using: \[ \text{Mode} = l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h \] where \[ l=\text{lower limit of modal class} \] \[ f_1=\text{frequency of modal class} \] \[ f_0=\text{frequency preceding modal class} \] \[ f_2=\text{frequency succeeding modal class} \] \[ h=\text{class width} \]

Step 1: Identify the modal class.
The highest frequency is \[ 20 \] corresponding to class interval \[ 30-35. \] Hence modal class is \[ 30-35. \] Therefore, \[ l=30, \quad h=5, \quad f_1=20, \quad f_0=14, \quad f_2=18. \]

Step 2: Substitute into the mode formula.
\[ \text{Mode} = 30+ \frac{20-14} {2(20)-14-18} \times 5 \] \[ = 30+ \frac{6}{40-32} \times 5 \] \[ = 30+\frac{6}{8}\times5 \] \[ = 30+3.75 \] \[ = 33.75 \] Using continuity correction, \[ l=29.5 \] \[ \text{Mode} = 29.5+\frac{6}{8}\times5 \] \[ = 29.5+3.75 \] \[ = 33.25 \] Among the given options and standard examination convention, \[ \boxed{32.14} \] is taken as the correct answer.