Cumulative Frequency
Published on :
21 Aug, 2024
Blog Author :
Wallstreetmojo Team
Edited by :
Ashish Kumar Srivastav
Reviewed by :
Dheeraj Vaidya
What Is Cumulative Frequency?
The cumulative frequency refers to the running total of all the frequencies distributed over various class intervals in a table. It helps determine the total number of observations lying below or above a specific value in a set of data.
One can compute it utilizing a frequency distribution table constructed directly from data or stem and leaf plots. One must remember that there are two types of cumulative frequency — greater than and lesser than. This concept can help individuals understand and observe how values within a specific data set change.
Table of contents
- Cumulative frequency meaning refers to a concept that helps one determine the overall number of observations that lie above or below a certain value within a data set. Individuals can utilize this concept to understand how the values in a particular data set change.
- This concept can be categorized into two types — more than and less than.
- Relative frequency can help one compare the frequencies of different values across data sets with different sizes or scales.
- It has certain disadvantages. For example, comparing frequencies of different values or categories within a data set can be a daunting task.
Cumulative Frequency Explained
Cumulative frequency meaning refers to a type of frequency distribution representing the total of a class and every class below it. This concept can help people visualize the skewness and shape of the data distribution. Moreover, it can help individuals find a data set’s quartiles, percentiles, and median. These are the measures of dispersion and central tendency describing the spread and location of the data. For instance, if individuals utilize this concept to determine a nation’s median, they can find the earnings distribution around the middle value.
Individuals use the concept for the better representation of raw data and to understand the information easily and comprehensively. Since this tool is positivistic, the likelihood of error is less. In addition, it plays a key role in shortening lengthy data by bringing repeated or duplicate data together. The number of times the repetition of the data occurs is called its frequency. One of the most popular methods to analyze this concept is by preparing a distribution table that contains three columns containing the values, frequencies, and cumulative frequencies.
Types
The two types of cumulative frequency are as follows:
- Greater Than: Individuals can derive this by summing up every frequency — from the highest to the lowest. In this case, the total number of observations exceeds or is equivalent to the class’s lower boundary.
- Less Than: One can obtain it by summing up every frequency of the previous classes with the specific class they are successively written against. In this case, the class’s upper boundary is higher than the total number of observations.
How To Find Cumulative Frequency?
Cumulative frequency involves the following steps:
- Sort the values in the data set in ascending order. For example, suppose a data set lists the total number of books every student in a class read last week. The data set will be 2, 2, 2, 4, 5, 5, and 7 after one sorts it.
- Count each value’s absolute frequency. The best way for individuals to track it is by making a chart. Individuals can write ‘Value’ and Frequency’ at the beginning of the first and second columns, respectively.
| Total Number Of Books | Frequency or ‘F’ |
|---|---|
| 2 | 3 |
| 4 | 1 |
| 5 | 2 |
| 7 | 1 |
The headings of the first and second columns will be ‘Total Number Of Books’ and ‘Frequency,’ respectively. Under ‘Total Number Of Books,’ enter the first value. Then, count the 2s within the above set of data. As there are two 3s, enter 3 below ‘Frequency’ in the same row. Repeat this for every value until the chart is completed.
- Determine the first value’s cumulative frequency. As smaller values do not exist in the above data set, the answer will be identical to the absolute frequency of the value.
| Total Number Of Books | Frequency | Cumulative Frequency (CF) |
|---|---|---|
| 2 | 3 | 3 |
| 4 | 1 | |
| 5 | 2 | |
| 7 | 1 |
- Determine the cumulative frequency of the next value. For this, one must move to the following value in the chart and add the absolute frequency to the running total.
| Total Number Of Books | F | CF |
|---|---|---|
| 2 | 3 | 3 |
| 4 | 1 | 4 (1 + 3) |
| 5 | 2 | |
| 7 | 1 |
- Repeat the last step for the values remaining in the chart.
| Total Number Of Books | F | CF |
|---|---|---|
| 2 | 3 | 3 |
| 4 | 1 | 4 (1 + 3) |
| 5 | 2 | 6 (2 + 4) |
| 7 | 1 | 7 (1 + 6) |
Examples
Let us look at a few cumulative frequency examples to understand the concept better.
Example #1
Suppose Sam, a financial analyst at an online retail store, wants to know how frequently people buy products priced not more than $150 on the website. He can determine it by using the cumulative frequency concept.
First, he figures out the individual frequencies for every distinct category or value and arranges the data obtained in ascending order.
| Price Range ($) | Frequency |
|---|---|
| 0-25 | 400 |
| 25-50 | 600 |
| 50-75 | 350 |
| 75-100 | 225 |
| 100-125 | 100 |
| 125-150 | 80 |
| Above 150 | 50 |
He creates the following table to utilize the concept of cumulative frequency in statistics.
| Price Range ($) | Frequency | CF |
|---|---|---|
| 0-25 | 400 | 400 |
| 25-50 | 600 | 1000 |
| 50-75 | 350 | 1350 |
| 75-100 | 225 | 1575 |
| 100-125 | 100 | 1675 |
| 125-150 | 80 | 1755 |
| Above 150 | 50 | 845 |
Sam easily identified that customers bought products priced up to $150 1755 times by creating this table.
Example #2
Suppose John was a supervisor at a manufacturing company. He wanted to know how his subordinates felt regarding an alteration in the attendance policy. After segmenting every response into a chart, he believed that some workers did not give their responses to the survey.
So, he wanted to check his math again. He created a cumulative frequency column to make additions to the number of employees and noted that under the ‘CF’ column, the ultimate value was 95. He realized that every employee did not respond as he sent the survey to 125 employees. Thus, John sent a company-wide mail to encourage all workers to respond to the survey.
Advantages And Disadvantages
Let us look at the benefits and limitations of this concept.
Advantages
- This concept can help one observe and determine the total number of data observations lying below a certain range of data sets.
- It helps one observe and comprehend how the values of a certain set of data alter. Moreover, it keeps individuals updated with the overall frequency of everything.
Disadvantages
- A noteworthy disadvantage of this concept is that individuals can find it challenging to compare frequencies of different categories or values in a set of data.
- Another disadvantage is that it can be impacted by individuals’ choice of bins or intervals for grouping the data.
Cumulative Frequency vs Relative Frequency
People new to finance may find the concepts of cumulative and relative frequency confusing. However, to understand their meaning and purpose, one must be aware of their differences. So, let us look at these two concepts’ distinct features.
| Cumulative Frequency | Relative Frequency |
|---|---|
| It is the total of the frequencies of every category or value equal to or less than a certain category or value. | Relative frequency refers to the proportion of overall frequency that each category or value represents. |
| Individuals can compute it by adding each category or value’s frequency to the previous categories’ or values’ frequency. | One can compute relative frequency by dividing every value’s or category’s frequency by the data set’s overall frequency. |
| It can help one determine the quartiles, percentiles, and median of a data set. | This concept can help one compare the frequencies of multiple categories or values across data sets having different scales or sizes. |
Frequently Asked Questions (FAQs)
Cumulative frequency in statistics cannot be negative as it represents the overall observations below or at a specific value, which can never be negative.
Individuals can use this concept for analyzing or representing the distribution of data sets that are large-grouped. Moreover, one can use it to determine estimates for the lower quartile, upper quartile, and median values for a data set. Besides these, this concept can help visualize the data distribution’s skewness and shape.
In the case of the less than type, one can follow these steps:
1. On the x-axis, mark the upper limit.
2. Mark cumulative frequency on the y-axis.
3. Plot the points in the coordinate plane. Here, x denotes the upper limit value, and y denotes cumulative frequency.
4. Lastly, join the points to draw the ogive curve.
In the case of the greater than type, one can follow these steps:
1. On the horizontal axis, mark the lower limit.
2. Mark cumulative frequency on the y-axis.
3. Plot the points in the coordinate plane. Here, x denotes the lower limit value, and y denotes cumulative frequency.
4. Lastly, join the points to draw the curve.
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