Ogive
- Visualizes cumulative counts (frequencies) of a dataset to show how totals accumulate across values or classes.
- Constructed by plotting cumulative frequency against the variable (often at class lower limits) and joining points with a smooth curve.
- Useful for reading percentiles, medians, or comparing distributions across groups or time.
Definition
Section titled “Definition”An Ogive is a graph that shows the cumulative frequency distribution of a continuous or discrete variable. It is a graph of the cumulative frequency distribution and is a smooth curve that represents the cumulative frequencies of the data set. It is also known as a cumulative frequency curve or a cumulative frequency graph.
Explanation
Section titled “Explanation”An Ogive displays, on the horizontal axis, the variable (individual values or class limits) and, on the vertical axis, the cumulative frequency for each value or class. Each cumulative frequency is obtained by adding the frequency of the current class to the cumulative total of all previous classes. The plotted points are joined with a smooth curve to form the Ogive, which represents how the total frequency accumulates across the range of the variable.
Construction steps (as given in the source):
- Draw the horizontal axis for the variable (e.g., marks).
- Draw the vertical axis for cumulative frequency.
- Mark the points on the horizontal axis corresponding to the lower limits of each class or the individual values.
- Mark points on the vertical axis corresponding to the cumulative frequency of each class or value.
- Join the points with a smooth curve.
Examples
Section titled “Examples”Example 1 (individual marks)
Section titled “Example 1 (individual marks)”Marks: 20, 25, 30, 35, 40, 45, 50, 55
Frequency: 2, 3, 4, 5, 6, 7, 8, 9
Cumulative Frequency: 2, 5, 9, 14, 20, 27, 35, 44
| Marks | Frequency | Cumulative Frequency |
|---|---|---|
| 20 | 2 | 2 |
| 25 | 3 | 5 |
| 30 | 4 | 9 |
| 35 | 5 | 14 |
| 40 | 6 | 20 |
| 45 | 7 | 27 |
| 50 | 8 | 35 |
| 55 | 9 | 44 |
Plotting the cumulative frequencies against the marks and joining the points with a smooth curve produces the Ogive.
Example 2 (class intervals)
Section titled “Example 2 (class intervals)”Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequency: 5, 10, 15, 20, 25, 30
Cumulative Frequency: 5, 15, 30, 50, 75, 105
| Marks | Frequency | Cumulative Frequency |
|---|---|---|
| 0-10 | 5 | 5 |
| 10-20 | 10 | 15 |
| 20-30 | 15 | 30 |
| 30-40 | 20 | 50 |
| 40-50 | 25 | 75 |
| 50-60 | 30 | 105 |
Construct the Ogive by plotting cumulative frequencies at the class lower limits and joining the points with a smooth curve.
Use cases
Section titled “Use cases”- Understanding the distribution or accumulation pattern of a variable.
- Making predictions about future totals based on accumulated counts.
- Comparing the distribution of a variable across different groups or over time.
Related terms
Section titled “Related terms”- Cumulative frequency distribution
- Cumulative frequency curve
- Cumulative frequency graph