1. What is Cumulative Frequency?

Cumulative frequency is the sum of all frequencies up to a certain point in a data set. It helps analyze how many observations fall below certain values and is fundamental in statistics for creating cumulative frequency tables and graphs.

2. How to Calculate Cumulative Frequency

The calculation is straightforward:

Where:

• \( f_i \) — Frequency of the ith observation
• \( n \) — Number of observations

Process: Start with the first frequency, then add each subsequent frequency to the running total to get the cumulative frequency for each point.

3. Importance of Cumulative Frequency

Details: Cumulative frequency is essential for:

• Creating ogives (cumulative frequency graphs)
• Determining percentiles and quartiles
• Analyzing data distribution
• Comparing different data sets

4. Using the Calculator

Tips:

• Enter frequencies separated by commas (e.g., 10, 15, 20, 25)
• Only numeric values are accepted
• The calculator will output the cumulative frequencies in order

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between frequency and cumulative frequency?
A: Frequency counts occurrences in each category, while cumulative frequency sums all frequencies up to that point.

Q2: How is cumulative frequency used in ogives?
A: Ogives plot cumulative frequencies against upper class boundaries to visualize data distribution.

Q3: Can cumulative frequency decrease?
A: No, cumulative frequency always increases or stays the same as you move through the data set.

Q4: What's the last cumulative frequency value equal to?
A: The last value equals the total sum of all frequencies in the data set.

Q5: How does cumulative frequency relate to percentiles?
A: Percentiles are found by determining where a certain percentage of the cumulative frequency occurs.