Question

Formula for finding mode for grouped data is:

• A. \( l + \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h \)
• B. \( l - \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h \)
• C. \( l - \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] - h \)
• D. None of these

Hint:

The formula for the mode of grouped data adjusts the position of the mode based on the frequencies of the modal class and its neighboring classes.

Answer 1

The Correct Option is B

Step 1: Formula for Mode for Grouped Data.
The formula for finding the mode for grouped data is: \[ \text{Mode} = l - \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h \] where:
\( l \) is the lower boundary of the modal class,
\( f_1 \) is the frequency of the modal class,
\( f_0 \) is the frequency of the class preceding the modal class,
\( f_2 \) is the frequency of the class succeeding the modal class,
\( h \) is the class width.
Step 2: Understanding the Formula.
This formula helps us find the mode when the data is grouped into class intervals. The mode is adjusted based on the frequencies of the modal class and its neighboring classes. 
Step 3: Conclusion.
Thus, the correct formula for finding the mode for grouped data is: \[ \text{Mode} = l - \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h \]