Question

In the formula, Mode = \(l + \left[\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right] \times h\), \(f_1\) is

• A. Frequency of the modal class
• B. Frequency of the class preceding the modal class
• C. Frequency of the class succeeding the modal class
• D. Frequency of the median class

Hint:

Formula for Mode of Grouped Data: \( \text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h \) - \(l\): Lower limit of modal class. - \(f_1\): Frequency of modal class. - \(f_0\): Frequency of class preceding modal class. - \(f_2\): Frequency of class succeeding modal class. - \(h\): Class size. The modal class is the class interval with the highest frequency.

Answer 1

The Correct Option is A

Step 1: Identify the terms in the formula for the mode of grouped data.
The formula for calculating the mode of a continuous grouped frequency distribution is: \[ \text{Mode} = l + \left[\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right] \times h \] where: - \(l\) = lower limit of the modal class.
- \(h\) = size of the class interval (assuming all class sizes are equal).
- \(f_1\) = frequency of the modal class (the class with the highest frequency).
- \(f_0\) = frequency of the class preceding the modal class.
- \(f_2\) = frequency of the class succeeding the modal class.

Step 2: Match \(f_1\) with its definition.
According to the standard definition of the terms in this formula, \(f_1\) represents the frequency of the modal class.
This matches option (1).