1. What is Mean of Grouped Data?

The mean of grouped data is the average value calculated from frequency distribution data. It represents the central tendency of the data set when individual values are grouped into classes or categories with corresponding frequencies.

2. How Does the Calculator Work?

The calculator uses the mean formula:

Where:

• \( f \) — Frequency (number of observations in each class)
• \( x \) — Midpoint (center value of each class interval)
• \( \sum(f \times x) \) — Sum of frequency multiplied by midpoint
• \( \sum(f) \) — Total frequency (sum of all frequencies)

Explanation: The formula calculates the weighted average where each class midpoint is weighted by its frequency.

3. Importance of Mean Calculation

Details: Calculating the mean of grouped data is essential in statistics for understanding the central tendency of large data sets that are organized into frequency distributions. It provides a single value that represents the entire data set.

4. Using the Calculator

Tips: Enter frequency and midpoint pairs separated by commas, one pair per line. For example: "5,10" for frequency 5 and midpoint 10. All frequencies must be non-negative numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between mean of grouped and ungrouped data?
A: Ungrouped data mean uses individual values, while grouped data mean uses class midpoints weighted by frequencies, providing an approximation when individual values are not available.

Q2: How accurate is the mean of grouped data?
A: It's an approximation that assumes all values in a class are equal to the midpoint. The accuracy depends on class width and data distribution.

Q3: When should I use grouped data mean instead of ungrouped?
A: Use grouped mean when working with frequency distributions or when individual data points are not available, only class intervals and frequencies.

Q4: What if my classes have different widths?
A: The mean calculation remains valid as long as you use appropriate midpoints for each class interval.

Q5: Can I use this for categorical data?
A: The mean of grouped data is typically used for numerical data. For categorical data, mode is more appropriate as a measure of central tendency.