Frequency Distribution Table

A frequency distribution table is a method for organizing data so it is easier to understand. It shows how often each value or category appears in a dataset.

The table usually has two or three columns:

• First column: Lists the values or class intervals (groups of values) depending on the data.
   
• Second column (optional): Which shows the tally marks for each value.
   

Third column: Shows the frequency, which is the number of times each value occurs.

What does “frequency” mean?

Frequency means how many times something occurs. For example, if your heart beats 72 times in a minute, the frequency is 72 beats per minute.

In everyday life, we come across lots of numerical information, like exam scores, temperatures, or game points. All this information is called data. After collecting data, we organize it using a frequency distribution table so that it becomes easier to read, understand, and analyze.

For example, suppose 8 children read the following number of books in a week: \(3, 2, 4, 3, 2, 3, 4, 2.\)

Solution:

Step 1: List the values from the given values 
2, 3, 4.

Step 2: Count the frequency of each value
 

This table shows that:

• 3 children read 2 books.
   
• 3 children read 3 books.
   
• 2 children read 4 books.
   

This table helps us to see clearly how many children read each number of books, making the data easier to understand.

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 example, 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. 

To convert a number into a percentage, we 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:

• Grouped Frequency Distribution

• Ungrouped Frequency Distribution

• Relative Frequency Distribution

• Cumulative Frequency Distribution
  
   

Grouped Frequency Distribution

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 as it makes the 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:
 

Ungrouped Frequency Distribution

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:
 

Relative Frequency Distribution

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 Distribution
 

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 from 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 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.

A frequency distribution table arranges the data to display how often each value or range occurs, making it easier to identify patterns, trends, and comparisons for better understanding and analysis.
 

• A frequency distribution table shows how many times each number or group of numbers comes up in the data.
   
• The key elements are the values or groups of values, how often they appear (frequency), the running total (cumulative frequency), and sometimes the percentage (relative frequency).
   
• Use real-life examples, such as daily study hours, the number of fruits eaten, or the number of toys owned, to improve understanding.
   
• Encourage the children to tally the data themselves to make the process interactive.
   
• Ensure all counts and calculations in a frequency distribution table are correct, as errors can lead to wrong interpretations of the data.
   
• Show students how to turn the frequency tables into bar graphs or histograms, which help them to understand the data better through clear visual patterns.
   
• Highlight the difference between grouped and ungrouped frequency tables, so students will know when and how to use each type.  

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, businesses use the frequency distribution table. It helps them track their sales and 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. 

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

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