Statistics-Cumulative Frequency Distribution

Let us look at the marks that ten students from a class have obtained in a science test. The marks are our raw data, and it is as follows:

32, 26, 12, 37, 24, 07, 31, 40, 22, 29.

After this, we will consider the statistical measure that we refer to as range. It is the difference that we get between the data set’s largest value and the smallest value. So, looking at the data above, we get the range of

40-07= 33

Now, you see how tough the process will get if there is a larger number. If one has to include the test marks of all 40 students in the class, it will be a complex process to understand and analyse all the data if it is not organised.

Therefore, statistical interpretation’s objective is to organise data into an accessible form to make it easier for us to understand and analyse it. Well-structured frequency distributions make these tasks a lot easier. 

Use of a Frequency Distribution Graph

It offers us a way of organising data to make it more meaningful. That is where preparing a 

frequency distribution graph is required. A frequency distribution chart will summarise all the data under two columns. They are variables/categories followed by their frequency. The first column will list all the results as individual values or in the coupled value; it all depends on the data set’s size. We use tally marks for representing frequency in the second table. Also, this column is optional. Finally, the frequency is noted in the third column. You must have also seen that there is a lot of information in our day-to-day lives in the form of graphs, tables, figures etc.

Data refers to the collection of bits of information, measurements or observations. And raw data is the initial collection of information. This information is still not organised. At the first step of collecting information, you will get raw data. For example, if you go around and ask any random five people their favourite colours, they provide you with the answers blue, green, yellow, red, white; this is raw data. 

Then there are two types of data, i.e., discrete and continuous data. A data set is called to be discrete if values belonging to a set are distinct and separate. It can’t be in decimals.

Example: No. Of students who cleared the Maths exam.

 Continuous data can be a whole number but not always; it can be in decimals also. Data is said to be continuous if data could take any value in a specified interval.

 Examples: Wind speed, Volts of electricity.

Frequency Distribution Graph:

It is often not easy to find the frequency of data from a vast dataset. So to make appropriate use of the data, we prepare frequency distribution graphs.

Types of Frequency Distribution Table:

The frequency distribution table provides us with the information of the collected data. There are various frequency distribution tables as per the representation of data. They include-

• Cumulative frequency distribution table
• Ungrouped frequency distribution table
• Relative frequency distribution table
• Grouped frequency distribution table
• Relative cumulative frequency distribution table.

The available kinds of frequency distribution tables include grouped frequency distribution tables. And ungrouped frequency distribution tables.

Applications of Frequency Distribution Table:

There are two kinds of frequency distribution tables. One is an ungrouped frequency distribution table, and the other is a grouped frequency distribution table. Further, let’s take a look at some of the observations that have been derived from the frequency distribution table method:

• In the table that we use to measure the data frequency, we can easily observe the number of times the data appears in the data that use frequency.
• The table assists in measuring the distribution, such as variance, range, and standard variation.
• The range refers to the variation between higher and lower values of the data provided.
• After that, the mean, median, and mode get measured.
• The table then assists in deciding the symmetry or asymmetry’s length.

Frequency Distribution Calculator

Frequency Distribution Calculator is the new method that illustrates the frequency distribution for the provided data set.

How to Use the Frequency Distribution Calculator

The method of using the frequency distribution calculator is as follows:

• Enter the data values divided by a comma in the input space.
• Now click the “Calculate Frequency Distribution Table” button to get the outcome.
• Finally, the new window will show the frequency distribution table for the given data.

Examples (illustrated) – Frequency Distribution Table:

Runs scored by Virat Kholi in 10 International matches are listed as follows:

100,99,98,95,100,98,95,95,100,90

Then the ungrouped frequency distribution table for the given data is as shown: 

Conclusion

The frequency distribution table in statistics allows finding the data in a simple tabular form. After looking at the frequency and tally marks, we learn that they are the fundamental features needed to construct a frequency distribution table. Also, representing data by using a frequency distribution table is very easy. The frequency distribution table’s applications and properties assist us in straightforwardly exploring the data features.