Frequency Distribution Table

Frequency Distribution Table in statistics is a table that contains all the values and frequencies of different objects. It is an efficient way to record and retrieve a big chunk of data. It helps in easy visualization of data based on its frequency which basically means how many times a particular data appears.

In this article, we will learn about, Frequency Distribution Table Definition, Examples, How to Make Frequency Distribution Table, and others in detail.

What is Frequency Distribution Table?

Frequency Distribution Table is a way of arranging data to make it more understandable. It consists of two main columns – one for variables or categories and another for their frequencies. Sometimes there’s a third column. The first column usually lists individual values or intervals, depending on the data size. The second column shows tally marks for each value, and optionally, there can be a third column for the frequency count of each value.

The term “frequency” means how often something happens. For instance, if your normal heartbeat is 72 beats per minute, 72 is the frequency because it’s how many times your heart beats in a minute.

For example, Jane throws a dice multiple times, noting the outcomes: 4, 6, 1, 2, 2, 5, 6, 6, 5, 4, 2, 3. To see how many times each number (1, 2, 3, 4, 5, 6) appears, she organizes them into categories using tally marks in a frequency distribution table.

Outcomes	Tally Marks	Frequency
1	I	1
2	III	3
3	I	1
4	II	2
5	II	2
6	III	3

Key Terms Associated with Frequency Distribution Table

The key terms related to frequency distribution table is defined below:

• Frequency Distribution Table: A chart that organizes data by listing variables or categories along with their respective frequencies. It helps in summarizing and understanding the data.
• Variables or Categories: The different values or groups of values in the data set that are listed in the first column of the frequency distribution table.
• Frequency: The number of times a specific variable or category occurs in the data set. It is recorded in the second column of the table.
• Ungrouped Frequency Distribution Table: A type of frequency distribution table where individual values are listed along with their frequencies without grouping them into intervals.
• Grouped Frequency Distribution Table: A type of frequency distribution table where values are grouped into intervals, and their frequencies are recorded. This is useful when dealing with a large range of values.
• Tally Marks: Marks used to represent the frequency of each variable or category in a compact and visual way. Tally marks are often included in a third column of the table.
• Total Frequency: The sum of all frequencies in the table. It provides an overall count of the data set and is sometimes included in the last row of the table.

How to Create a Frequency Distribution Table

Constructing a frequency distribution table is simple, follow the steps given below:

Step 1: Create a table with two columns – one for the title of the data you’re organizing and the other for frequency. Optionally, add a third column for tally marks.

Step 2: Examine the items in the data and decide whether to create an ungrouped or grouped frequency distribution table. If there are many different values, it’s usually better to opt for a grouped table.

Step 3: Fill the first column with the values from the data set.

Step 4: Count how often each item repeats in the collected data. In simpler terms, find the frequency of each item by counting.

Step 5: In the second column, write the frequency corresponding to each item.

Step 6: In the last row of the table, include the total frequency.

Frequency Distribution Table in Statistics

A Frequency Distribution Table in statistics is like a summary that organizes data into categories or intervals, showing how many times each category occurs. It helps make sense of large sets of information by presenting it in a more manageable form. This table simplifies data analysis, making it easier to understand patterns and trends.

Cumulative Frequency Distribution Table

A Cumulative Frequency Table helps organize and summarize data by showing how many observations are below or equal to specific values. It includes a running total of frequencies as you go through the data, making it easier to analyze patterns and understand the distribution of values.

Example: Given the marks of 20 students in maths exam as: 68, 72, 75, 78, 80, 82, 85, 88, 90, 92, 68, 72, 75, 78, 80, 82, 85, 88, 90, 92

Solution:

Step 1: Arrange the given data into ascending order as: 68, 68, 72, 72, 75, 75, 78, 78, 80, 80, 82, 82, 85, 85, 88, 88, 90, 90, 92, 92

Step 2: Create a frequency distribution table

Marks	Frequency
68	2
72	2
75	2
78	2
80	2
82	2
85	2
88	2
90	2
92	2

Step 3: Add the adjacent frequency in the cumulative frequency column

Marks	Frequency	Cumulative Frequency
68	2	2
72	2	4
75	2	6
78	2	8
80	2	10
82	2	12
85	2	14
88	2	16
90	2	18
92	2	20

The Cumulative Frequency column is the running total of frequencies. For example, at the score of 82, the cumulative frequency is 12, meaning 12 students scored 82 or below.

Step 4: Interpretation

10 students scored 80 or below.

16 students scored 88 or below.

All 20 students took the exam, so the cumulative frequency at the highest score (92) is 20.

What is Grouped Data?

Grouped data is a way of organizing information when dealing with a large set of values. Instead of listing each individual value, the data is grouped into intervals or ranges. These intervals have a specific width and cover a range of values. For example, if you have data representing ages, instead of listing each age individually, you might group them into ranges like 0-10, 11-20, 21-30, and so on.

Frequency Distribution Table for Grouped Data

A grouped frequency distribution table is a way of organizing data based on class intervals. In this type of table, the data categories are divided into various class intervals with the same width. For instance, intervals like 0-10, 10-20, 20-30, and so on. The frequency of each class interval is then recorded against the respective interval. Let’s consider a different example to illustrate this concept:

Class Intervals	Frequency
Total= 35
10-20	3
20-30	7
30-40	12
40-50	5
50-60	8

What is Ungrouped Data?

Ungrouped data is a form of organizing information where each individual value is listed separately without being grouped into intervals. Each distinct value in the data set is presented individually. This type of representation is common when dealing with a relatively small set of data.

Components of a Frequency Distribution Table

Various components of Frequency Dristribution Table are,

Class Intervals

• Class intervals in a frequency distribution table represent the ranges or groups into which the data is organized. These intervals help simplify the presentation of large datasets.
• For example, if you’re dealing with ages, you might have intervals like 0-10, 11-20, and so on. The class intervals organize the data into manageable groups, making it easier to understand.

Frequency

• Frequency is the number of times a particular value or class interval occurs in the dataset. It is listed in the frequency column of the table.
• For each class interval, the frequency indicates how many times the values fall within that range. This information helps in understanding the distribution pattern of the data.

Cumulative Frequency

• Cumulative frequency is the running total of frequencies as you move through the class intervals in the table. It starts from the first class interval and progressively adds up the frequencies of each interval.
• Cumulative frequency is useful in analyzing the overall distribution and identifying patterns. It is often included as a separate column in the frequency distribution table.

Relative Frequency

• Relative frequency expresses the proportion of the total dataset that a particular class interval or value represents. It is calculated by dividing the frequency of a class interval by the total number of observations and is often presented as a percentage.
• Relative frequency provides insights into the proportional significance of each interval in relation to the entire dataset.

Types of Frequency Distributions

There are two types of frequency distributions that are,

• Simple Frequency Distribution
• Cumulative Frequency Distribution
• Relative Frequency Distribution

Now lets learn about them in detail.

Simple Frequency Distribution

A simple frequency distribution is a basic type where the data is organized into non-overlapping class intervals, and the frequency of each interval is listed. Each class interval represents a range of values, and the corresponding frequencies show how many times values fall within those ranges. This type provides a clear overview of the distribution of data.

Cumulative Frequency Distribution

In a cumulative frequency distribution, the frequencies are accumulated or added up as you move through the class intervals. The cumulative frequency of a particular interval includes the frequencies of all the previous intervals. This type helps in understanding the total occurrence of values up to a certain point in the dataset and is useful for analyzing the overall pattern of the data.

Relative Frequency Distribution

A relative frequency distribution expresses the proportion of the total dataset that each class interval represents. It is calculated by dividing the frequency of each interval by the total number of observations. This type provides a percentage or decimal representation of the contribution of each interval to the overall dataset. It helps in comparing the importance of different intervals in relation to the entire dataset.

Uses of Distribution Frequency Tables

Distribution frequency tables are helpful in organizing and presenting data in a clear way. They show how often different values or groups of values appear in a set of data. This can be useful in various fields:

1. Organizing Information: Frequency tables help arrange data systematically, making it easier to understand and interpret.
2. Identifying Patterns: By displaying how frequently values occur, these tables assist in spotting patterns or trends in the data.
3. Summarizing Data: They provide a concise summary of the distribution of values, helping to grasp the overall picture without going through individual data points.
4. Statistical Analysis: Frequency tables are foundational for statistical analysis, aiding in computations of measures like mean, median, and mode.
5. Comparison: They allow for a quick comparison of different groups or categories, enabling effective decision-making.
6. Research and Surveys: In research and surveys, frequency tables simplify the representation of collected data, aiding researchers in drawing conclusions.
7. Data Interpretation: These tables serve as a basis for further data interpretation and drawing insights, supporting informed decision-making.
8. Visualizing Data: They can be used to create charts and graphs, turning raw data into visual representations for easier comprehension.
9. Quality Control: In manufacturing or quality control processes, frequency tables help in monitoring and maintaining product quality by analyzing defects or variations.
10. Educational Purposes: Frequency tables are valuable for educational purposes, teaching students the basics of data analysis and interpretation.

Read More,

• Grouping of Data
• Frequency Distribution

Solved Examples on Frequency Distribution Table in Statistics

Example 1: Suppose you have a dataset of exam scores: {65, 72, 85, 90, 78, 92, 88, 76, 82, 95, 68, 74, 80}. Create a grouped frequency distribution table with class intervals of width 10 starting from 60.

Solution:

Class intervals	Frequency
60-70	2
70-80	4
80-90	5
90-100	2

• The first class interval (60-70) includes scores 65 and 68.
• The second class interval (70-80) includes scores 72, 78, 76, and 74.
• The third class interval (80-90) includes scores 85, 90, 88, 82, and 80.
• The fourth class interval (90-100) includes scores 92 and 95.

Example 2: In a survey, participants were asked to rate a product on a scale of 1 to 5. The data collected is as follows: {3, 4, 5, 2, 3, 4, 5, 1, 3, 4, 5, 2, 4, 5, 1}. Create a relative frequency distribution table to represent the proportion of each rating in the dataset.

Solution:

Step 1: Identify unique values and their frequencies.

Rating	Frequency
1	2
2	2
3	3
4	4
5	4

Step 2: Calculate the relative frequency for each rating.

Relative Frequency = (Frequency of Rating) / (Total Number of Ratings)

Rating	Frequency	Relative Frequency
1	2	2/15
2	2	2/15
3	3	3/15
4	4	4/15
5	4	4/15

Step 3: Optionally, present the relative frequency as a percentage.

Relative Frequency (Percentage) = Relative Frequency × 100

Rating	Frequency	Relative Frequency	Relative Frequency (%)
1	2	2/15	13.33
2	2	2/15	13.33
3	3	3/15	20
4	4	4/15	26.67
5	4	4/15	26.67

Practice Questions on Frequency Distribution Table in Statistics

Q1. Consider the dataset: 7, 9, 5, 7, 2, 9, 3, 5, 7, 9. Create an ungrouped frequency distribution table for these values.

Q2. For the dataset representing the ages of a group of people: 15, 18, 22, 25, 28, 32, 35, 38, 42, 45, 48, 52, 55, create a grouped frequency distribution table with class intervals of width 5 starting from 15.

Q3. Using the dataset: 4, 7, 4, 6, 8, 7, 9, 5, 8, 6, calculate the cumulative frequency and relative frequency for each class interval in a grouped frequency distribution table with intervals 4-5, 6-7, and 8-9.

FAQs on Frequency Distribution Table in Statistics

1. What is Frequency Distribution Table?

A Frequency Distribution Table shows how often different values occur in a set of data. It lists the values along with their corresponding frequencies or counts.

2. What is Importance of a Frequency Distribution Table?

The Importance of a Frequency Distribution Table is that it helps organize and summarize data. It makes it easier to see patterns and trends in the information.

3. What are Types of Frequency Distribution Table?

There are two main Types of Frequency Distribution Tables:

• Grouped Frequency Distribution Table
• Ungrouped Frequency Distribution Table

4. How to Make Frequency Distribution Table?

Frequency Distribution Table can be made by selecting a suitable class interval and assigning the number of data set falling in that particular class interval.

5. What is a Frequency Distribution Table Maker?

A Frequency Distribution Table Maker is a online tool that make a frequency distribution table based on input data