Cumulative Frequency Calculator Grouped Data

Cumulative Frequency Formula:

\[ CF = \sum f \text{ up to class}, \text{Running total of frequencies.}, CF \text{ (count)}, f \text{ (frequency up to class)} \]

Cumulative Frequencies:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Cumulative Frequency?

Cumulative frequency is the running total of frequencies through the classes in ascending order. It shows the total number of observations that lie below the upper boundary of each class interval in a frequency distribution.

2. How Does The Calculator Work?

The calculator uses the cumulative frequency formula:

\[ CF = \sum f \text{ up to class}, \text{Running total of frequencies.}, CF \text{ (count)}, f \text{ (frequency up to class)} \]

Where:

\( CF \) — Cumulative frequency
\( \sum f \) — Sum of frequencies up to the current class
\( f \) — Frequency of each class

Explanation: The calculator takes individual frequencies and calculates their cumulative sum progressively, showing how frequencies accumulate across classes.

3. Importance Of Cumulative Frequency

Details: Cumulative frequency is essential for constructing ogives (cumulative frequency curves), calculating percentiles, quartiles, and analyzing data distribution patterns in statistics.

4. Using The Calculator

Tips: Enter frequencies as comma-separated values (e.g., 5,10,15,20). All frequencies must be non-negative integers representing the count of observations in each class.

5. Frequently Asked Questions (FAQ)

Q1: What Is The Difference Between Frequency And Cumulative Frequency?
A: Frequency shows the count for each individual class, while cumulative frequency shows the running total of frequencies up to and including each class.

Q2: How Is Cumulative Frequency Used In Statistics?
A: It's used to create cumulative frequency curves (ogives), determine medians, quartiles, percentiles, and analyze data distribution patterns.

Q3: Can Cumulative Frequency Decrease?
A: No, cumulative frequency always increases or stays the same as you move through classes, since it's a running total that accumulates frequencies.

Q4: What Is The Maximum Cumulative Frequency?
A: The maximum cumulative frequency equals the total number of observations in the dataset, which is the sum of all individual frequencies.

Q5: How Do I Interpret Cumulative Frequency Results?
A: Each cumulative frequency value represents the total number of observations that fall below the upper boundary of that particular class interval.