Frequency Distribution Table
A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.
What is a Frequency Distribution Table?
A frequency distribution table is a way to organize data so that it makes the data more meaningful. A frequency distribution table is a chart that summarizes all the data under two columns - variables/categories, and their frequency. It has two or three columns. Usually, the first column lists all the 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 is optional.
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.
In our day-to-day 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 frequency distribution table is one of the ways to organize data.
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 draw a frequency distribution table with tally marks.
|2||I I I||3|
|6||I I I||3|
The table above is an example of a frequency distribution table. You can observe that all the data that was collected has been organized under three 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, the frequency distribution table in statistics helps us to condense data in a simpler form so that it is easy for us to observe its features at a glance.
How to Construct a Frequency Distribution Table?
It is easy to make a frequency distribution table by using the steps given below:
- Step 1: Make a table with two columns - one with the title of the data you are organizing and the other column will be for frequency. [Draw three columns if you want to add tally marks too]
- Step 2: Look at the items written in the data and decide whether you want to draw an ungrouped frequency distribution table or a grouped frequency distribution table. If there are too many different values, then it is usually better to go with the grouped frequency distribution table.
- Step 3: Write the data set values in the first column.
- Step 4: Count how many times each item is repeating itself in the collected data. In other words, find the frequency of each item by counting.
- Step 5: Write the frequency in the second column corresponding to each item.
- Step 6: At last you can also write the total frequency in the last row of the table.
Let's look at an example. 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)|
The frequency distribution table drawn 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 get 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 such a frequency distribution table, first, write the 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.
|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|
A frequency distribution table drawn above is called a grouped frequency distribution table.
What is Frequency Distribution Table 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 table 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 mid-points of the bars in a histogram.
Frequency Distribution Table for Grouped Data
A frequency distribution table for grouped data is known as a grouped frequency distribution table. It is based on the frequencies of class intervals. As it is already discussed above that in this table, all the categories of data are divided into different class intervals of the same width, for example, 0-10, 10-20, 20-30, etc. And then the frequency of that class interval is marked against each interval. Look at an example of the frequency distribution table for grouped data given in the image below.
Cumulative Frequency Distribution Table
Cumulative frequency means the sum of frequencies of the class and all the classes below it. It is calculated by adding the frequency of each class lower than the corresponding class interval or category. An example of a cumulative frequency distribution table is given below:
Cumulative frequency distribution table calculators 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 Related Articles
Check these articles related to the concept of a frequency distribution table in math.
Frequency Distribution Table Examples
Example 1: A school conducted a blood donation camp. The blood groups of 30 students were recorded as follows.
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
Represent this data in the form of a frequency distribution table.
Solution: The above data can be represented in a frequency distribution table as follow:
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 distribution table with class intervals of equal widths, starting from 25 - 30, 30 - 35, and so on. Also, find the range of weekly pocket expenses.
Solution: The following table represents the given data:
Weekly expenses (in $) Number of students 25-30 2 30-35 4 35-40 10 40-45 4 45-50 5 Total 25
In the given data, the smallest value is 26 and the largest value is 49. So, 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 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.
Values Frequency 1 1 2 1 3 3 4 1 5 2 6 0 7 1 8 1 9 2 10 0 Total 12
FAQs on Frequency Distribution Table
What is Frequency Distribution Table?
A frequency distribution table is a tabular representation of the frequencies of the categories given. It represents the data in an organized manner that is useful for the graphical representation of data or to calculate mean, median, and mode, variance, etc. It has generally two columns, one is of the categories of data set, and the other one is of the frequency of each category. Sometimes, a tally marks column is also added before frequency that helps to count the frequency.
What is the Use of a Frequency Distribution Table?
A frequency distribution table is useful to perform calculations on the given data. It involves calculations involving measures of central tendency, variance, statistical tests, and analysis. Apart from that, a frequency distribution table is useful to represent the data in a neat manner that is easy to understand.
How to Make an Ungrouped Frequency Distribution Table?
To make an ungrouped frequency distribution table, follow the steps given below:
- Identify all the categories that are given in the data.
- Draw a table with two columns - one is of categories and another is of their respective frequencies. Draw three columns if you want to add tally marks too.
- Write each category in a separate row in column 1.
- Count the number of times they are occurring or repeating themselves in the collected data.
- Write those frequencies for each category in column 2.
What is Grouped Frequency Distribution Table?
A grouped frequency distribution table is a table that represents categories in the form of class intervals. It is mainly used with large data sets.
What is cf in Frequency Distribution Table?
In a frequency distribution table, cf means cumulative frequency. Cf represents the collective or total frequency of a category and all the categories lower or greater than that.
How to Interpret Frequency Distribution Table?
The following points must be kept in mind while interpreting a frequency distribution table:
- The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.
- The number written on the right of each category is its frequency. It lies in the same row.
- There are no other category lies except the ones written in the first column of the table.
How to Draw Frequency Distribution Table?
There are mainly two or three columns in a frequency distribution table - column 1 for categories, column 2 for tally marks, and column 3 for frequency. So, to draw a frequency distribution table, we have to write data in this order only. First, we identify all the categories or class intervals, then we write them in separate rows in column 1. After that, we focus on each category one by one and count their frequencies. We write their respective frequency in the third column. This is how we can draw a frequency distribution table.
How to Get Class Boundary in Frequency Distribution Table?
A class boundary is a number that separates the class intervals without leaving any gaps. For example, if the two subsequent class intervals are given as 20-29 and 30-39. The class boundary is calculated as (upper limit of the first class interval + lower limit of the second class interval)/2. So, here class boundary = (29+30)/2, which is equal to 29.5.
What are the Types of Frequency Distribution Table?
There are mainly three types of frequency distribution table, which are given below:
- Ungrouped frequency distribution table
- Grouped frequency distribution table
- Cumulative frequency distribution table