Cumulative Frequency Solved Examples
Various examples on Cumulative frequency are,
Example 1: Below is the data of math test results of students of class VII. Draw a Cumulative frequency table for the given data.
Marks | 50 | 60 | 70 | 80 | 90 |
---|---|---|---|---|---|
Number of students | 5 | 8 | 12 | 6 | 4 |
Solution:
We total the frequencies as we proceed down the table to determine the cumulative frequency. This is how it is calculated:
Score | Frequency | Cumulative Frequency |
---|---|---|
50 | 5 | 5 |
60 | 8 | 13 |
70 | 12 | 25 |
80 | 6 | 31 |
90 | 4 | 35 |
Example 2: A group of students’ results on a science test are displayed in the table below. Find the cumulative frequency.
Score | Frequency |
---|---|
60 | 4 |
70 | 7 |
80 | 9 |
90 | 6 |
100 | 4 |
Solution:
Determine the cumulative frequency:
Score | Frequency | Cumulative Frequency |
---|---|---|
60 | 4 | 4 |
70 | 7 | 11 |
80 | 9 | 20 |
90 | 6 | 26 |
100 | 4 | 30 |
Example 3: In a group setting, students were asked how many hours they spent on homework each week. Determine the more than cumulative frequency of the given data.
Hours | Frequency |
---|---|
1-5 | 7 |
5-10 | 12 |
10-15 | 9 |
15-20 | 5 |
20-25 | 3 |
Solution:
We begin by computing the cumulative frequency in order to determine the more than cumulative frequency.
First, determine the cumulative frequency:
Hours | Frequency | Cumulative Frequency |
---|---|---|
1-5 | 7 | 7 |
5-10 | 12 | 19 |
10-15 | 9 | 28 |
15-20 | 5 | 33 |
20-25 | 3 | 36 |
Now, Determine the frequency that is more than cumulative:
Hours (Class Interval) | Hours | Frequency | More than Cumulative Frequency |
---|---|---|---|
1-5 | More than 1 | 7 | 36 |
5-10 | More than 5 | 12 | 36-7 = 29 |
10-15 | More than 10 | 9 | 29-12 = 17 |
15-20 | More than 15 | 5 | 17-9 = 8 |
20-25 | More than 20 | 3 | 8-5 = 3 |
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