In this lesson, you will be introduced to the concept of frequency distribution. Right from representing class performances in schools to representing statistical data in other fields, there are several applications of frequency distribution tables and graphs. When it comes to finance, frequency distributions are used by traders to make note of the prices and other details and also identify trends. Therefore, it is an important concept in Math.
You can get a brief idea about frequency distribution by exploring the simulation shown above. As you go through this lesson, you will learn how to create a frequency distribution table and the formulas and graphs related to frequency distributions.
Let's begin!
Lesson Plan
Frequency
Do you know the meaning of "frequency?"
Frequency indicates how often something occurs.
For example, your heartbeat is 72 heartbeats/min under normal conditions.
Frequency corresponds to the number of times a value occurs.
Here are a few examples.
Annie takes music class once every week.
Thus, frequency = 1
Annie takes dance classes as per the following schedule: 1 lesson each on Mondays, Wednesdays, and Fridays.
Thus, frequency per week = 3
What Is Frequency Distribution?
In our daytoday lives, we come across a lot of information in the form of numerical figures, tables, graphs, etc.
This information could be marks scored by students, temperatures of different cities, points scored in matches, etc.
The information that is collected is called data.
Once the data is collected, we have to represent it in a meaningful manner so that it can be easily understood.
The data should be organized in such a way that all its features are summarized in a table and a glance of it should be enough to understand the data.
How do we go about doing this?
The frequency distribution is one of the ways to organize data.
We will learn all about it here.
Frequency Distribution Calculator
Let's first explore the frequency distribution calculator below.
Enter the data and observe how the frequency distribution table is created.
Frequency distribution table calculators such as the one above save a lot of time when tabulating the data.
It makes calculations easy and leads to the organization of data in seconds.
Frequency Distribution Table
A frequency distribution table is a way to organize data so that it makes the data more meaningful.
Here's a frequency distribution table example for you to understand this concept better.
Jane is fond of playing games with dice.
She throws the dice and notes the observations each time.
These are her observations:
4, 6, 1, 2, 2, 5, 6, 6, 5, 4, 2, 3
To know the exact number of times she got each digit (1, 2, 3, 4, 5, 6) as the outcome, she classifies them into categories.
An easy way is to use tally marks.
Note that a diagonal line across 4 vertical lines counts as 5
Outcomes  Tally Marks  Frequency 

1  I  1 
2  I I I  3 
3  I  1 
4  I I  2 
5  I I  2 
6  I I I  3 
The table above is known as a frequency distribution table.
You can observe that all the data that was gathered has been organized under two columns.
Thus, a frequency distribution table is a chart summarizing the values and their frequencies.
In other words, it is a tool to organize data.
This makes it easy for us to understand the given set of information.
Thus, frequency distribution in statistics helps us condense data in a simpler form so that it is easy for us to observe its features at a glance.
 When dealing with quantitative data, we divide them into categories or class intervals. Does the same follow for qualitative data as well?
How Do You Construct a Frequency Distribution Table?
Let's look at an example.
Meet Ms. Jennifer and her assistant, Mr. Thomas.
Ms. Jennifer is a teacher.
She wants to look at the marks obtained by the students of her class in the last exam.
She does not have the time to go through each test paper individually to see the marks.
Thus, she asks Mr. Thomas to organize the data in a table so that it is easier for her to look at everyone's marks together.
Ms. Jennifer suggests using a frequency distribution table to organize the data, so as to get a better picture of the data rather than using a simple list.
Using a frequency distribution table here is a good way to present the data as it will show Ms. Jennifer all the students' marks in one table.
But how can a frequency distribution table be created?
Mr. Thomas works hard to put together all the data.
The following table shows the test scores of 20 students, i.e., for one class.
Marks obtained in the test  Number of students (Frequency) 

9  1 
11  4 
13  1 
18  1 
20  1 
21  2 
22  1 
23  3 
25  1 
26  3 
29  1 
30  1 
Total  20 
A frequency distribution table such as the one above is called an ungrouped frequency distribution table.
It is the representation of ungrouped data and is typically used when you have a smaller data set.
Imagine how difficult it would be to create a similar table if you have a large number of observations, for example, the marks of students of three classes.
The table we will obtain will be quite lengthy and the data will be confusing.
Hence, in such cases, we form class intervals to tally the frequency for the data that belongs to that specific class interval.
To make a frequency distribution table, first write the categories or class intervals in one column.
Next, tally the numbers in each category based on the number of times it appears.
Finally, write the frequency in the final column.
The frequency is the total.
Marks obtained in the test  Number of students (Frequency) 

0  5  3 
5  10  11 
10  15  12 
15  20  19 
20  25  7 
25  30  8 
Total  60 
A frequency distribution table such as the one above is called a grouped frequency distribution table.

The frequency distribution formula is as follows: Divide the number of categories/values into intervals, then count the number of results in each interval. These number of times or occurrences represent frequency.

There are two easy ways to create a frequency distribution table in excel: COUNTIFS Function and FREQUENCY Function.

R is a widelyused statistical programming language. It is a tool for data processing and analysis. When you have a limited number of values (different values) in R, a quick summary of the data can be found by calculating a frequency table.
How Do You Describe a Frequency Distribution Table?
A frequency distribution table is a chart that summarizes all the data under two columns, values, and their frequency.
We have already learned the construction of the frequency distribution table in the section above.
It has two or three columns.
The first column lists all the various outcomes as individual values or in the form of class intervals, depending upon the size of the data set.
The second column includes the tally marks of each outcome.
The third column lists the frequency of each outcome.
Also, the second column can be optional.
What Is Frequency Distribution in Statistics?
Frequency distribution in statistics is a representation of data displaying the number of observations within a given interval.
The representation of a frequency distribution can be graphical or tabular.
Now let us look at another way to represent data i.e., graphical representation of data.
This is done using a Frequency Distribution Graph.
Such graphs make it easier to understand the collected data.
 Bar graphs represent data using bars of uniform width with equal spacing between them.
 A pie chart shows a whole circle, divided into sectors where each sector is proportional to the information it represents.
 A frequency polygon is drawn by joining the midpoints of the bars in a histogram.
 Data includes figures or numbers collected for some definite purposes.
 Frequency is the number that tells how often a particular entry occurs.
 There are two types of frequency distribution tables  Grouped Frequency Distribution Table and Ungrouped Frequency Distribution Table.
 Data can be represented using tables and graphs as well histograms, pie charts, frequency polygons, and so on.
Statistics and Probability
Frequency distribution in statistics is related to the probability distribution.
A frequency distribution represents the number of times of an occurrence.
A probability distribution represents the probability of occurrence.
The higher the frequency in any interval, the higher will be its probability to be chosen or selected.
There is a difference between relative frequency and probability.
The formula for relative frequency is given as \(\dfrac {f }{n}\).
A relative frequency table is a chart that shows the mode of a certain type of data based on the population sampled.
Solved Examples
Example 1 
A school conducted a blood donation camp.
The blood groups of 30 students were recorded as follows.
Represent this data in the form of a frequency distribution table.
Solution
Blood Group  Number of students 

A  9 
B  6 
AB  3 
O  12 
Total  30 
Example 2 
Given below are the weekly pocket expenses (in $) of a group of 25 students selected at random.
37, 41, 39, 34, 41, 26, 46, 31, 48, 32, 44, 39, 35, 39, 37, 49, 27, 37, 33, 38, 49, 45, 44, 37, 36
Construct a grouped frequency table with class intervals of equal widths, such as 25  30, 30  35, and so on.
Also, find the range of weekly pocket expenses.
Solution
Weekly expenses (in $)  Number of students 

2530  2 
3035  4 
3540  10 
4045  4 
4550  5 
Total  25 
The range of the weekly pocket expenses = 49  26 = $23
Example 3 
Silvia and Ashley have a set of number cards with numbers from 1 to 10
They take out a number card and write the number that comes up.
They continue doing the same for at least 12 times.
They get the following values:
5, 8, 9, 2, 3, 7, 3, 4, 5, 9, 3, 1
Construct a frequency table to arrange the data in better form.
Solution
Values  Frequency 

1  1 
2  1 
3  3 
4  1 
5  2 
6  0 
7  1 
8  1 
9  2 
10  0 
Total  12 
Example 4 
There are 20 students in a class.
The teacher, Ms. Jolly, asked the students to tell her their favorite subject.
She then constructed a frequency distribution table to get a clear idea.
Which is the mostliked subject?
How many students mentioned Science as their favorite subject?
Solution
Mathematics is the mostliked subject.
5 students mentioned Science as their favorite subject.
Example 5 
On World Environment Day, 100 schools decided to plant 100 tree saplings in their gardens.
The following data shows the number of plants that survived in each school after one month.
95  67  28  32  65  65  69  33  98  96 

76  42  32  38  42  40  40  69  95  92 
75  83  76  83  85  62  37  65  63  42 
89  65  73  81  49  52  64  76  83  92 
93  68  52  79  81  83  59  82  75  82 
86  90  44  62  31  36  38  42  39  83 
87  56  58  23  35  76  83  85  30  68 
69  83  86  43  45  39  83  75  66  83 
92  75  89  66  91  27  88  89  93  42 
53  69  90  55  66  49  52  83  34  36 
Using this data, can you find the number of schools that were able to retain 50% of the plants or more?
Solution
We need to represent this large amount of data in such a way that a reader can understand it easily.
To include all the observations in groups, we will create various groups of equal intervals.
These intervals are called class intervals.
From this table, it is clear that 50% or more plants survived in (8 + 18 + 10 + 23 + 12) schools.
\(\therefore\) 71 schools were able to retain 50% or more plants in their garden. 
Interactive Questions
Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.
Let's Summarize
We hope you enjoyed learning about the frequency distribution table with the simulations and practice questions. Now, you will be able to easily solve problems on relative frequency distribution table, how to make a frequency distribution table, frequency distribution formula, frequency distribution graph, frequency distribution table calculator, frequency distribution table example, frequency distribution table definition, frequency distribution table in r, frequency distribution table for grouped data.
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Frequently Asked Questions (FAQs)
1. What are the various graphs that can be created for a frequency distribution table?
Bar graph, line graph and pie chart are the graphs that can be created for a frequency distribution table.
2. How can you organize data?
Data can be organized with the help of charts and graphs for better visualization. You can use bar graphs, frequency charts, picture graphs, and line graphs for organizing data.