Frequency Distribution Table

In a dataset, how often something occurs is expressed by its frequency. In statistics, frequency distribution is a tool that is used for data organization and to make meaningful decisions. How often a value appears in a dataset can be understood by a frequency distribution. It shows where the most values are concentrated and where the least values are presented. Tabularly or graphically, we can represent the frequency distribution.

To visually represent a frequency distribution table, we use a frequency distribution graph. Graphical elements, such as bars, lines, and curves are used to express how frequently various values occur. These graphs help us to simplify complex data, figure out new trends, and make informed decisions. The various methods for representing the frequency distribution are:

Histogram 

A histogram is used for representing numerical data, and it is similar to a bar graph. The y-axis of the histogram indicates frequencies, and the x-axis represents interval classes. Remember, there is no gap between the bars of a histogram. For example, here is a frequency table explaining the number of survey respondents in each age group.

The histogram showing the ages of survey respondents is:

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Bar graph

Bar graphs use rectangular bars to represent the data on the x-axis and y-axis. The height and length of the bars show the frequency of categories or values. The bar graph is commonly used to express the frequency of ungrouped data in a flexible sequence. Remember to always leave gaps between the bars to separate the categories clearly. For e.g., the distribution table representing a dataset of kids and their favorite ice cream flavors will look like this:

The following is a bar graph representing the frequency of kids and their favorite ice cream flavors.

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Frequency polygon 

In a frequency polygon, the data is visually represented by plotting dots at the midpoints of each class interval and joining them with straight lines to form a polygon. For example, here is a dataset that shows the number of young people enjoying different genres of movies.

Here is the frequency polygon, representing the frequency of youth and their favorite movie genres. 

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Pie chart

The pie chart represents data in a circular format. Each category is represented as a slice of an entire circle, and the size of each slice shows its proportion of the total dataset. For example, the frequency distribution table of kids who prefer different fruits is given below:

Here, the pie chart of the given frequency distribution table is given below. 

Here, when we convert a number into a percentage, use the formula:
Percentage = Frequency of a category / Total frequency × 100 
So, total frequency = 8 + 5  + 7 + 4 + 6 = 30

Frequency of Apple = 8 / 30 × 100 = 26. 7%

Frequency of Orange = 5/ 30 × 100 = 16.7%

Frequency of Pineapple = 7/ 30 × 100 = 23.3%

Frequency of Strawberry = 4 / 30 × 100 = 13.3%

Frequency of Mango =  6 / 30 × 100 = 20

Depending on the nature of the collected data, frequency distribution is classified into different types. The collected data is organized in a meaningful way to clearly understand the nature, pattern, and trends and to make better decisions. The four types of frequency distribution are:

The observations or data in a grouped frequency distribution are divided into different intervals. Then, the frequencies of each class interval are counted. When we have a very large set of data, this type of frequency distribution is useful to make data much easier to understand.

For example, the data given in a grouped frequency distribution is categorized into different groups of equal sizes. Then, the number of times each class interval or category appears is marked against each interval. The frequency distribution table for grouped data is given below:

In an ungrouped frequency distribution, the distinct observations or data are collected and counted separately. When we have a small dataset, the ungrouped frequency distribution is useful. For instance, if we have to count the marks of 15 students in a class, we can apply this type of frequency distribution. The frequency distribution table of an ungrouped dataset is:

The percentage or proportion of observations in each class is represented by relative frequency distribution. We use this type of distribution to compare several data sets or to understand the distribution of data within a single set by expressing frequencies as percentages. The formula for relative frequency is:
Relative frequency = Frequency of event / total number of events
For example, the relative frequency distribution table for the following data is:

 The relative frequency distribution table:

Cumulative frequency is the running total of all frequencies up to a specific value or interval. The two types of cumulative frequency distributions are:

• Less than cumulative frequency
  It refers to the sum of all frequencies up to and including a given interval. 

• More than cumulative frequency
  It refers to the sum of all the frequencies from a given interval onward. 
  For example, we collected the values of marks scored by Miya on her last 18 exams.

Here, we have a lot of distinct values. So, we will categorize these values in a grouped distribution frequency table.

Next, we can convert this frequency distribution table into a cumulative frequency distribution table.

Next, the cumulative frequency distribution of the second type which is more than cumulative frequency.

While making a frequency distribution table, we have to adhere to several steps. They are as follows:

Step 1: Design a table with two columns. One for frequency and the other for the data we need to organize. 

Step 2: Decide whether we need a grouped frequency distribution table or an ungrouped frequency distribution table by analyzing the items in the given dataset. When we have a very large set of data, then better we go with a grouped frequency distribution table. 

Step 3: In the first column, categorize the data set values. 

Step 4: Identify the frequency of each category by counting them and allocate it to the second column. 

Step 5: Finally, write the total frequency in the last row of the frequency distribution table. 

By following these steps, we can create an organized and well-structured frequency distribution table for the given dataset.

Frequency distribution is a tool used in statistics to organize data and make insightful conclusions. A frequency distribution table is a chart that presents the frequency of each category or data in an organized way. It represents how often each value occurs in a given dataset. The real-life applications of the frequency distribution table are countless. They are given below.

• To determine the number of goods and services sold by a shop or company, the businesses use the frequency distribution table. It helps them track their sales and to analyze the feedback of their customers. 

• In the field of education, teachers and educational institutions can categorize the marks of their students and analyze the performance of the students. They can keep records of the marks scored by the students in each examination. 

• To track the frequency of a disease based on age, blood groups, or patient locations, hospitals, and healthcare professionals use the frequency distribution table. 

• To evaluate the income levels in a population, categorize expenditure levels, and analyze stock prices within a certain range, political critics, government officials, and economists can use the frequency distribution table for their research and studies. 

• In the fields of sports, public transportation, and social media, the frequency distribution table plays a vital role in organizing data into several categories.