1. What is Mode for Grouped Data?

The mode for grouped data is the value that appears most frequently in a data set when the data is organized into classes or intervals. It represents the peak of the frequency distribution.

2. How Does the Calculator Work?

The calculator uses the mode formula for grouped data:

Where:

• \( L \) — Lower limit of the modal class
• \( f_m \) — Frequency of the modal class
• \( f_1 \) — Frequency of the class preceding the modal class
• \( f_2 \) — Frequency of the class succeeding the modal class
• \( h \) — Class interval width

Explanation: The formula estimates where the mode would be within the modal class based on the frequencies of neighboring classes.

3. Importance of Mode Calculation

Details: The mode is important in statistics as it identifies the most common value in a data set. For grouped data, it helps identify the most frequent range or category.

4. Using the Calculator

Tips: Enter the lower limit of the modal class, the frequency of the modal class, frequencies of adjacent classes, and the class width. All values must be valid (frequencies ≥ 0, class width > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between mode for raw data and grouped data?
A: For raw data, mode is simply the most frequent value. For grouped data, we estimate the mode within the modal class using neighboring frequencies.

Q2: When should I use grouped data mode?
A: Use it when working with continuous data that has been grouped into classes, or when you only have access to frequency distribution tables.

Q3: What if two classes have the same highest frequency?
A: The data set is bimodal. You would need to calculate mode for both modal classes separately.

Q4: How accurate is the grouped data mode?
A: It's an estimate. The actual mode might differ slightly, especially if the data isn't normally distributed.

Q5: Can the mode be outside the modal class?
A: No, the formula ensures the mode always falls within the modal class boundaries.