Frequency Distribution Table
In our everyday lives, collecting, recording, and maintaining information is indeed a crucial task. When it comes to the field of mathematics, statistics has an integral part as it refers to the organization, distribution, collection, and interpretation of the set of observations or data (representation of facts or a piece of information that can be further processed). With the help of statistics, we can have a better understanding of what a dataset or a set of observations reveals about a specific phenomenon. We can also predict the nature of data using statistics, by studying large amounts of data and trends and also by interpreting the results. We have various methods for representing the statistical data, including pie charts, bar graphs, tables, histograms, frequency polygons, amongst many others. So, let us now discuss the concepts of collecting and recording data using a frequency distribution table.
For having a better understanding of the frequency distribution, let us consider an example. Suppose we have the marks obtained by ten students out of 25 in a unit test conducted at their school as follows:
12, 23, 22, 8, 19, 15, 24, 25, 17, and 9
The data given above is in the raw form and is referred to as the raw data. We can calculate its range, which is the difference between the largest value and the smallest value in a set of observations or data set. In this particular scenario, the range is 25-8 = 17.
Understanding the Frequency Distribution Table
Without any second thoughts, the process or representation of data explained in the example above would become way more difficult and cumbersome if there were a larger number of observations in a set. In such cases, the concept of a frequency distribution table proves to be exceedingly beneficial as it organizes a larger data set into a table and makes the interpretation and analysis a lot easier and convenient.
Ungrouped Data
Let us consider a situation in which the scores of 20 students out of 25 in their mathematics unit test are given as follows:
15, 18, 21, 24, 18, 11, 15, 21, 13, 9, 23, 14, 6, 18, 20, 11, 10, 20, 25, and 17
Please keep in mind that the term 'frequency' denotes the number of times an observation appears or occurs in a dataset. Hence, it is quite evident that the frequency shall increase in the case of repetitions. Now, let us draw the frequency distribution table for the given dataset.
Student Marks
In this example, the frequency refers to the number of students scoring the same marks in the mathematics unit test. It is imperative to note that the sum of the frequencies should be equal to the total number of observations in the dataset. The frequency distribution table of this example is known as an ungrouped frequency distribution table as it takes into consideration the ungrouped data and calculates the frequency of every observation one by one.
Grouped Data
Let us consider another situation in which we have the scores of 200 students instead of 20 students out of 25 in their mathematics unit test. It will prove to be a hectic task of tallying the scores of all the 200 students. Moreover, the length of the table will increase as well, and it will not at all be understandable. In such cases, the concept of a grouped frequency distribution table becomes handy as it considers groups or data in the form of class intervals for tallying the frequency of observations like which observation belongs to a specific class interval.
For having a better understanding of a grouped frequency distribution table, take a look at the table given below based on the dataset of the previous section.
Marks Obtained by Students in Unit Test
The first column of the grouped frequency distribution tables denotes the scores of students represented in the form of class intervals. "Lower Limit" is the lowest number in the class interval, and "Highest Limit" is the highest number in the class interval. The example explained above falls under the case of continuous class intervals as the upper limit of a specific class is the lower limit of the next class.
In the case of continuous class intervals, the extreme values are included or counted in that class interval where they are the lower limit, for instance - if there is a student who has scored ten marks in the mathematics unit test, then his marks would be counted or included in the class interval 10-15 and not 5-10.
Disjoint class intervals are analogous to continuous class intervals, in which the class intervals will be of the form 0-3, 4-7, 8-11, and so on, and their frequency distribution table is constructed in the same manner as explained above.
Solved Example
Consider the frequency distribution table given below corresponding to the marks scored by students in their science unit test out of 20 and answer the questions that follow.
Student Marks
Question 1
Find out the lower limit of the second-class interval?
Answer 1
The lower limit of the second-class interval, that is, 5-10, is 5.
Question 2
What is the class size?
Answer 2
The class size refers to the difference between the upper- and lower-class limits, which is 5-0 = 5 or 10-15 = 5 (the answer is 5 in all the cases).
Question 3
What is the class mark for the interval 10-15?
Answer 3
The average of the upper and the lower limit is the class mark. So, for the interval 10-15, the class mark is \[\frac{(10+15)}{2} = \frac{25}{2} = 12.5\].
Question 4
What are the class limits of the second interval?
Answer 4
The class limits of the second interval, that is, 5-10 are 5 (lower limit) and 10 (upper limit).
Key Takeaways
In statistics, a frequency distribution is a visual depiction of the number of observations within a certain interval.
Normal distributions, which display the observations of probabilities divided across standard deviations, benefit from frequency distributions in particular.
A frequency distribution can be represented graphically or tabulated to make it easier to understand.
Grouped Frequency Distribution and Ungrouped Frequency Distribution are the two forms of frequency tables.
Traders utilize frequency distributions to track market activity and spot patterns in finance.
FAQs on Frequency Distribution Table Statistics
1. How can I construct a Frequency Distribution Table?
Follow the below steps to make a frequency distribution table:
Step 1 - Create a table with two columns: one for the title of the data you're collecting and the other for frequency. If you wish to include tally marks, make three columns.
Step 2 - Ascertain whether you want to construct an ungrouped frequency distribution table, or a grouped frequency distribution table based on the items written in the data. If there are too many distinct values, the grouped frequency distribution table is typically the preferable choice.
Step 3 - In the first column, write the values from the data collection.
Step 4 - Count the number of times each item appears in the gathered data. In other words, count the number of times each item appears.
Step 5 - Fill in the second column with the frequency for each item.
Step 6 - Finally, in the table's last row, you may enter the overall frequency.
These procedures for creating a frequency distribution table are for an ungrouped frequency distribution table. It is the representation of ungrouped data and is often employed when the data collection is small. To create a table for a large number of observations, you should form class intervals to tally the frequency for the data that belongs to that specific class interval. To create a table like this, start by writing the class intervals in one column. Finally, in the last column, write down the frequency.
2. In statistics, what is a Frequency Distribution Table?
Statistics is the gathering, presentation, analysis, organisation, and interpretation of facts or data. Using statistics, we may make predictions about the nature of data based on past data. Statistics are useful when studying and observing vast amounts of data. In statistics, a frequency distribution is a data representation that shows the number of observations within a fixed period. A frequency distribution can be represented graphically or tabularly. This is accomplished through the use of a frequency distribution table graph. Such graphs aid in the comprehension of the collected data. Data is represented in bar graphs by bars of consistent width with equal space between them. The mid-points of the bars in a histogram are joined to form a frequency polygon. A pie chart depicts an entire circle divided into sectors, each of which is proportionate to the information it displays.
3. How Should a Frequency Distribution Table Be Interpreted?
A frequency table is a method of summarizing data by illustrating the number of occurrences of a data variable. When evaluating a frequency distribution chart, keep the following aspects in mind:
The first column is normally for the data set's categories, while the second or third column is generally for the frequency of each category.
The frequency of each category is indicated by the number placed to the right of its name. It is in the same row.
There are no additional categories of lies than those shown in the table's first column.
4. What are the types of Frequency Distribution Tables?
The frequency distribution table presents information from the gathered data in a well-designed tabular format, allowing for easy analysis of the data. There are several sorts of frequency distribution tables based on how the data is represented. They are:
Ungrouped frequency distribution table - It displays the frequency of an item in each particular data value as opposed to groupings of data values.
Grouped frequency distribution table - The data is sorted and segregated into groups called class intervals in this.
Cumulative frequency distribution table - In a frequency distribution, it is the sum of the first frequency and all frequencies below it.
Relative frequency distribution table - It indicates the percentage of total observations linked with each category.
Relative cumulative frequency distribution table.
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