Cumulative Frequency distribution

Cumulative Frequency is a term that refers to the frequency of an event across time. The total of a frequency and all frequencies in a frequency distribution until a specific determined class interval is the cumulative frequency starting with the first and ending with the last. The total, as well as the data, are shown in a table, with the frequencies grouped into class intervals. Let’s look at cumulative frequency, producing a cumulative frequency graph, and reading a cumulative frequency table, as well as some instances.

 Cumulative Frequency Definition:

In statistics, the first-class interval’s frequency is added to the second-class interval’s frequency, and this sum is added to the third class, and so on; frequencies produced this way are known as cumulative frequencies (c.f.). A cumulative frequency distribution or cumulative frequency table is a table that presents cumulative frequencies that are distributed over multiple classifications. Cumulative frequency is divided into two categories: lesser than type and greater than type. Let’s look at a few instances that are commonly employed in real-life scenarios.

 Example 1: Robert works for a toy manufacturer as a sales manager. When he looks at his quarterly sales records, he notices that in the month of April, he sold a total of 83 toy cars. 

Because all frequencies have already been added to the previous total, the latest cumulative total will always equal the total for all observations. 83=20+30+15+18 in this case. 

Because all frequencies have already been added to the previous total, the latest cumulative total will always equal the total for all observations. 83=20+30+15+18 in this case

: Various Cumulative Frequency Types

Cumulative frequency is a table that displays cumulative frequencies dispersed in class intervals. lesser than and greater than. Let’s look at both frequency

Cumulative Frequency is lower than Lesser Frequency. 

Lesser than cumulative frequency is calculated by accumulating the frequencies of all previous classes, including the class against which it is written, in that order. The cumulate begins with the smallest size and progresses to the largest. In other words, it is called lesser than cumulative frequency when the number of observations is less than the upper boundary of a class.

 : Frequency that is greater than the cumulative frequency 

Finding the cumulative total of frequencies from the highest to the lowest class yields greater than cumulative frequency. It’s also known as cumulative frequency of more than one type. In other words, it is deemed greater than cumulative frequency when the number of observations is greater than or equal to the lower boundary of the class.

 : Constructing a Cumulative Frequency

A frequency for a variety of values or categories. There are a few procedures that can be taken to create a cumulative frequency distribution table, making it simple to create. 

Step 1: Create a frequency distribution table with the continuous variables and a suitable class lengsteps

step 2: Calculate the frequency of each of the class intervals. 

Step 3: For each class interval, find the endpoint (upper limit or lower limit). 

Step 4: Add the numbers in the frequency column to get the cumulative frequency. 

Step 5: Make a table with all of the results.

 Graphing the Cumulative Frequency Distribution 

A graph can be used to depict the cumulative frequency distribution of grouped data. A cumulative frequency curve, often known as an ogive, is a type of representative graph. The most effective approach to analyse and extract results from cumulative frequency data is to represent it on a graph. Graphs, in particular, are particularly significant in the realm of statistics because they help us interpret and understand the data. So, let’s look at how the cumulative frequency is represented graphically. Cumulative Frequency Curves (or Ogives) come in two varieties: More than type Cumulative Frequency Curve and Less than type Cumulative Frequency Curve are two different types of Cumulative Frequency Curve.

: Frequency Curve

 in the more than cumulative frequency curve, or ogive. By subtracting the sum from the first-class frequency, the second-class frequency, and so on, the curve or ogive is formed. The result of the upward cumulation is equal to or larger than the cumulative curve. The following are the steps to plot a more than curve or ogive: 

Step 1: Draw a line on the x-axis to indicate the lower limit. 

Step 2: On the y-axis, write the cumulative frequency

Step 3: use a smooth freehand curve to connect the spots.

: Curve of Cumulative Frequency Less Than

We utilise the upper limit of the class to plot a curve on the graph in the mess than cumulative frequency curve or ogive. By adding the first-class frequency to the second-class frequency to the third-class frequency, and so on, the curve or ogive is formed. The cumulative frequency curve is less than the downward cumulation result. To plot a less-than-cumulative frequency curve, or ogive, follow these steps: 

Step 1: Draw a line on the x-axis to indicate the top limit. 

Step 2: On the y-axis, write the cumulative frequency.  

Step 3: Use a smooth freehand curve to connect the spots.

: Curve or ogive is less than: 

On the x-axis, write the upper limits of class intervals, and on the y-axis, write the less than type cumulative frequencies. Points (20,4), (40,9), (60,15), and (80,18) are plotted on the graph for plotting the less than type curve, and these are linked by freehand to form the less than ogive.

: Curve or ogive is less than: 

On the x-axis, write the upper limits of class intervals, and on the y-axis, write the less than type cumulative frequencies. Points (20,4), (40,9), (60,15), and (80,18) are plotted on the graph for plotting the less than type curve, and these are linked by freehand to form the less than ogive.

Conclusion:

The frequency, proportion, or percentage of cases with a given score or less is reported in cumulative frequency distributions. As a result, the cumulative frequency of a score is computed as the sum of the frequencies of all scores with a lower value plus the frequency of that score. Cumulative frequency distributions are typically shown using tables and graphs, and they can be created for both ungrouped and grouped scores.