Cumulative Relative Frequency

Data values of less than or equal to a certain value are considered cumulative relative frequency. Percentages are usually used to express it.

In a test of 100 marks, for example, assume that 60 marks have a cumulative frequency of 85%. A total of 85% of students scored less than 60 on the test.

Cumulative relative frequency explained with the help of table.

How to find the cumulative relative frequency?

  1. Create a frequency distribution table based on the data. 
  2. Sum the frequencies of the current class interval and the preceding class intervals to find the cumulative frequencies.
  3. Total frequency divided by cumulative frequency. Our cumulative relative frequency is the result of this calculation.
  4. Multiply the proportion by 100 to convert the cumulative relative frequencies into percentages if needed.

Calculate Cumulative Relative Frequency

Data sets are compiled by statisticians or scientists based on the frequency of measurements or responses to survey questions.  This is simply an item that appears in the set. When we compile a result in arrange table, the cumulative frequency of each item is the sum of all frequencies that come before this frequency. Sometimes data needs to establish the relative frequency for each data item, relative frequency is obtained by the frequency of each item by a total number of measurements.

How to calculate cumulative relative frequency

The cumulative relative frequency of each measurement or response depends not only on the number of occurrences but also on the relationship between the values of those responses. Using simple arithmetic, you fill out the other columns after entering the data items in the first column.

  1. Select a table of four columns. The first column is for data result, the second for frequency of each data result, the third for relative frequency, and the fourth column for cumulative relative frequency. Depending on whether you calculate them as fractions or percentages, the sum of frequencies in the second column equals the total number of measurements or responses. Data item 10 in the table has a cumulative relative frequency of one, or 100 percent.

Numbers or ranges of numbers can be entered in this column. When studying the heights of soccer players, for instance, each entry may represent one particular height or a range of heights. The table is divided into rows based on each entry.
Data items are categorized based on how frequently they appear in the data set.
Based on the number of observations, the relative frequency of each data item is calculated. Fractions or percentages can be used to express this number.
It is the cumulative frequency of each data item that is calculated by summing the relative frequencies of all the items before it and adding them together. When item three is added to items one and two, the cumulative relative frequency equals the sum of their relative frequencies.

Cumulative Relative Frequency Graph

A Graphically representing the cumulative relative frequency distribution for a quantitative variable, the cumulative relative frequency graph.

Cumulative Relative Frequency Distribution

The cumulative relative frequency distribution represents a collection of data in a tabular format showing the relative frequency of items below or equaling the upper class limit of each class. It is a measure of the proportion or fraction of the total number of instances of something

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Azhar Ali

Azhar Ali

Mathematician and Blogger.

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