Cumulative Frequency Curve
A cumulative frequency curve, also known as an ogive, graphically depicts the cumulative frequency distribution of a dataset. Plotting the cumulative frequencies against the upper-class boundaries or the midpoints of the class interval yields a smooth curve.
To generate a cumulative frequency curve, perform the subsequent steps:
- Step 1: Put the data in ascending order in your dataset.
- Step 2: To acquire cumulative frequency, gradually add up the frequencies.
- Step 3: Determine the axes’ scale by consulting your data.
- Step 4: For every data value and its cumulative frequency, plot points on the graph.
- Step 5: Connect the spots with a gentle freehand curve.
- Step 6: Put “Data Values” on the x-axis and “Cumulative Frequency” on the y-axis. Put a heading on the chart.
Cumulative frequency curve can be further plotted in two ways:
- Less than cumulative frequency Curve
- More than cumulative frequency Curve
Example: Draw a Less than and More than Cumulative Frequency Curve for the below given data:
| Class intervals | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequency (Students) | 5 | 8 | 12 | 15 | 20 |
Solution:
Calculating the cumulative frequency for less than curve:
| Class intervals | Frequency | Cumulative Frequency |
|---|---|---|
| less than 10 | 5 | 5 |
| less than 20 | 8 | 13 |
| less than 30 | 12 | 25 |
| less than 40 | 15 | 40 |
| less than 50 | 20 | 60 |
Now, we graph the cumulative frequencies about the class interval upper bound.
Now, calculate the cumulative frequency for more than one curve:
| Class Intervals | Frequency | Cumulative Frequency |
|---|---|---|
| more than 0 | – | 60 |
| more than 10 | 5 | 60-5=55 |
| more than 20 | 8 | 55-8=47 |
| more than 30 | 12 | 47-12=35 |
| more than 40 | 15 | 35-15=20 |
| more than 50 | 20 | 20-20=0 |
Now, we graph the cumulative frequencies about the class interval lower bound.
Also Check: Cumulative Frequency Curve
Cumulative Frequency
Cumulative Frequency: In statistics, cumulative frequency is defined as the sum of frequencies distributed across various class intervals. This involves organizing the data and their totals into a table where the frequencies are allocated according to each class interval.
In this article, we will cover a thorough explanation of cumulative frequency, cumulative frequency curve, formula, and a few examples based on it for better understanding.
Table of Content
- What is Cumulative Frequency?
- Cumulative Frequency Formula
- Cumulative Frequency Distribution
- Types of Cumulative Frequency
- How to Calculate Cumulative Frequency?
- Cumulative Frequency Table
- Cumulative Frequency Curve
- Cumulative Frequency Polygon
- Cumulative Frequency Graph
- Relative Frequency
- Cumulative Frequency Solved Examples
- Cumulative Frequency Practice Problems