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Best Frequency Distribution Table Examples for Grouped & Ungrouped Data

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January 23, 2025 Samuel Education

In mathematics and statistics, a frequency distribution table is an effective tool for organizing and streamlining data for simpler comprehension. These tables offer a clear view of data distribution, making it easy for analysts to see trends and patterns whether working with raw numbers or grouped intervals. They convert complicated information into representations that are easy to use, which makes them popular in a variety of domains, including corporate analytics and scholarly research. For both professionals and students, knowing how to build and comprehend these tables is crucial. With an emphasis on both grouped and ungrouped data, this blog provides a thorough overview of frequency distribution tables. To improve your learning, we will discuss their importance, offer detailed instructions for creating them, and offer real-world examples. We'll also go over how Mathematics Assignment Help may help you overcome obstacles and grasp this essential idea, guaranteeing that you acquire the abilities required for both scholastic and professional accomplishment.

Difference Between Grouped and Ungrouped Data Shared by Assignment Help Australia!

Effective dataset organization, analysis, and interpretation in statistics depend on knowing the distinction between grouped and ungrouped data. As per the mathematics assignment help, these two methods of data display have different functions and are appropriate for various kinds of analysis.

Definition

  • Data that has been arranged into categories or intervals is referred to as grouped data. Because of its condensed presentation, it is simpler to spot patterns and trends in big datasets.
  • Raw data that hasn't been classified or condensed is known as ungrouped data. It depicts unique observations in their unaltered state.

Presentation

  • A frequency distribution chart that breaks the data into class intervals and shows the frequency of each interval is commonly used to display grouped data.
  • Ungrouped data is presented as a straightforward list or array of observations that have not been categorized or summarized.

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Use Cases

  • Large datasets where the general distribution is more significant than individual values are best analyzed using grouped data. The test results of 1,000 pupils, for instance, were categorized into intervals like "50-60" or "60-70."
  • Smaller datasets with substantial individual values are better suited for ungrouped data. A list of test results from a class of 20 pupils, for example.

Analysis

  • For huge datasets, grouped data that has been summarized and condensed makes it simpler to compute statistical measures like mean, median, and mode.
  • Direct calculation from individual values is required for ungrouped data analysis, which can take a long time for big datasets.

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Data Representation

  • Since these visual aids correspond with categorized intervals, histograms, bar graphs, and pie charts are frequently used to depict grouped data.
  • Line graphs or scatter plots can be used to illustrate individual data points in ungrouped data.

Examples

  • Example of Grouped Data: In a survey of 200 respondents, the ages may be divided into groups such as 0–10, 11–20, and so on.
  • Example of Ungrouped Data: Ten pupils in a class with ages of 12, 14, 15, 11, 16, etc.

Steps to Create a Frequency Distribution Table Compiled by Assignment Help Australia!

A straightforward yet effective method for organizing and summarizing data is a frequency distribution table. It gives a concise summary of the frequency with which each data point or range of data points occurs within a dataset. You may create an effective frequency distribution table using the following procedures, regardless of whether you are dealing with grouped or ungrouped data.

Step 1: Understand the Data

Examine your dataset to determine its kind (qualitative or quantitative) and range before generating a table. Determine if a frequency table for grouped or ungrouped data is required.

Step 2: Determine the Range

Subtract the lowest number from the greatest to determine the range for quantitative data. All of the issues or confusions related to the assignment are resolved directly during the weekly live sessions organized by Assignment Help Australia.

Example: If your data points are 5, 15, 20, 25, and 35, the range is 35−5=30

Step 3: Choose the Number of Classes

Choose the number of intervals (classes) to use for grouped data. Generally speaking, depending on the size of the dataset, 5 to 20 intervals should be used.

Step 4: Calculate Class Width

To determine the class width, divide the range by the number of classes. If necessary, round up to the closest whole number.

Formula: Class Width = Number of Classes/ Range

Example: If the range is 30 and the number of classes is 5, the class width is 6.

Step 5: Create Class Intervals

To generate intervals, begin with the smallest data value and add the class width repeatedly. Make sure the intervals don't overlap. If you are struggling with completing your assignment, you can always opt for our assignment help Australia. 

Example: For a class width of 6, intervals could be 5−10, 11−16, 17−22, and so on.

Step 6: Tally the Frequencies

Count the number of data points that belong to each class interval after going through the dataset. To keep the count organized, use tally markers.

Step 7: Complete the Table

Make columns for the frequency counts, tally marks, and class intervals. To make sure the total equals the amount of data points in the dataset, add up the frequency column.

Step 8: Add Cumulative Frequency (Optional)

According to our assignment help Australia, add the frequency of each class to the total of all prior classes to determine the cumulative frequency for further information.

Step 9: Verify and Visualize

Verify the correctness of your data and table again. To graphically depict the table, you may optionally utilize visual aids like bar graphs or histograms.

These procedures will help you make a frequency distribution table that is easy to understand and arrange, which will make data analysis easier. Our Mathematics Assignment Help professionals can help you if you need individualized support or are having trouble with frequency tables, making sure your assignments are thorough and accurate.

Examples of Frequency Distribution Tables Shared by Assignment Help Australia

Frequency distribution tables help in systematically arranging data so that trends and patterns can be interpreted. The following are some examples of frequency distribution tables, both grouped and ungrouped, to further illustrate their use:

Example of Ungrouped Data

Each value and its frequency are recorded separately when working with ungrouped data.

Dataset: Test scores of 10 students: 7,8,7,9,10,8,7,10,9,8

Score

Frequency

7

3

8

3

9

2

10

2

The second column is determined by the frequency of each possible score in the set. This approach works best with tiny datasets. Our assignment help Australia also conducts regular guided sessions for students to provide them with a better understanding of the subject matter

Example of Grouped Data

A bigger dataset may be handled and analyzed more easily when it is divided into intervals using grouped data.

Dataset: Heights (in cm) of 20 students:

150, 152, 153, 155, 158, 160, 161, 162, 163, 165, 167, 170, 172, 173, 175, 177, 180, 182, 183, 185

Steps to Create the Table:

  • Range: 185−150=35
  • Number of classes: 5
  • Class width: ⌈35/5⌉=7

Height (cm)

Frequency

150–156

5

157–163

5

164–170

4

171–177

4

178–185

2

With a width of 7, heights are categorized into intervals (class intervals). The number of students whose heights fall within each interval is displayed in the frequency column. Get access to samples and guides created by our experts by opting for our assignment help Australia.

Cumulative Frequency Table

By summing the frequencies of all previous classes, the cumulative frequency may be computed for more information.

Height (cm)

Frequency

Cumulative Frequency

150–156

5

5

157–163

5

10

164–170

4

14

171–177

4

18

178–185

2

20

Understanding the distribution of data up to each class interval is made easier by the cumulative frequency column.

How Mathematics Assignment Help Australia Can Support You?

It might be difficult to understand mathematical concepts like frequency distribution tables, grouped data, and ungrouped data. Professional math assignment help providers may provide dependable assistance in this situation. They can help in the following ways:

Expert Guidance on Complex Topics

Experts in mathematics simplify difficult ideas like frequency distribution, cumulative frequency, and data arrangement into manageable stages. This guarantees that you fully understand the material and use it successfully.

Customized Solutions for Assignments

The Assignment Help Australia solutions are customized to match your unique needs and academic level, regardless of whether your assignment entails creating grouped data tables, resolving statistical issues, or examining data patterns.

Examples and Practice Problems

Math assignment aides improve your comprehension by offering real-world examples and extra practice problems, which increases your confidence in managing related activities on your own.

Step-by-Step Explanations

To help you understand the process rather than simply the result, each solution comes with thorough step-by-step instructions. Long-term comprehension and skill development are promoted by this approach.

Timely Delivery of Assignments

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Availability of Online Support

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In mathematics and statistics, frequency distribution tables are essential tools for organizing and interpreting data. Gaining proficiency in the construction and comprehension of these tables may greatly improve your analytical abilities, regardless of whether you're dealing with grouped or ungrouped data. To assist you in better comprehending this idea, this blog has given you the necessary procedures, distinctions, and examples.

However, don't be afraid to get expert help if you're having trouble handling the complexity of your math homework. Our assignment help Australia services, which include professional advice, tailored solutions, and prompt assistance, are intended to make your educational path easier. Allow us to assist you in overcoming obstacles in your academic career and confidently achieving your objectives. To begin your journey to success in mathematics, get in touch with us right now!

Author Bio

Samuel

"I am a seasoned Ph.D. scholar with deep expertise with years of rigorous research, publication, and teaching experience, I bring a wealth of knowledge and analytical acumen to complex academic challenges. My work focuses on delivering innovative solutions, advancing knowledge, and fostering academic excellence. Skilled in research methodology, data analysis, and scholarly writing, I have contributed to peer-reviewed journals and mentored students to achieve academic success.

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