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Frequency distribution tables are one of the most crucial topics in the field of Statistics. If you are studying statistics frequency distribution, the chances are that you may be asked to solve mathematical problems based on this idea. Most of the students flinch at the thought of working on frequency tables because it consists of different categories and too many numbers. Therefore, we have narrowed down the information on the frequency table in this blog. Read on to understand the basic overview and how to solve mathematical problems based on frequency table definition. If you are not knowing “how to calculate frequency distribution?” You are at right platform. Here, you will come to know everything about frequency distribution tables.
Let us consider frequency distribution examples to understand the frequency distribution table definition better. Say the marks obtained by 10 students in a class are as follows:
23, 26, 11, 18, 09, 21, 23, 25, 22, 11
This is known as raw data. Usually, statistics students are asked to determine the range of a frequency distribution. The range is the difference between the largest and smallest number in a given set of data. In the example given above, range = 26 – 09 = 17.
The above calculation was easier since there were limited observations. But what do you do when you have to deal with the frequency distribution for several observations? In that case, you need to use the frequency distribution table.
The table consists of categorical variables and quantitative variables. The categorical variables define categories such as (in this case) subjects like math and history. Quantitative variables define the numbers as shown below in the table.
| Subjects (Categorical variables) | No. of students pursuing the subject (Quantitative variables) |
| Maths | 14 |
| Chemistry | 58 |
| History | 1 |
| English | 4 |
| Total | 77 |
Table 1: Frequency distribution table showing categorical variables
The table mentioned above shows the subject in the left column and the number of students who pursue the respective subjects in the right column. A frequency distribution table gives you a snapshot of the data that let you find patterns in the data sets. For instance, we can understand from the above table that only a few students pursue history in the future.
The two main categories of frequency distribution table are:
Say, for instance, you have been asked to gather data on the test scores of 100 students. It will be quite tricky to tally the scores of all the 100 students. The table will also be huge in length and complicated to understand. That is when we use the grouped frequency tables.
In this case, we need to consider the groups of data in regular class intervals. Then we can tally the frequency for the data that belongs to a specific class interval.
Here is grouped frequency distribution table example:
| Marks obtained in the test [Class Interval] | Number of students [frequency] |
| 0-5 | 4 |
| 5-10 | 11 |
| 10-15 | 35 |
| 15-20 | 34 |
| 20-25 | 7 |
| 25-30 | 9 |
| Total | 100 |
Table 2: Grouped Frequency Distribution Table
In the example shown above, the left column consists of the marks obtained in the class interval form. The lower limit is the smallest number in the interval, and the upper limit is the highest number in the range. Thus, if there is a student who has scored 6 marks in the test, her marks would be included in the interval (5-10).
Let’s assume that the scores of 20 students are as follows:
23, 26, 11, 18, 09, 21, 23, 30, 22, 11, 21, 20, 11, 13, 23, 11, 29, 25, 26, 26
Now, remember that frequency is the number of times a certain observation has appeared in a set of data. Thus, if a number is repeated, its frequency increases.
Look at the table for better understanding:
| Marks | Number of students |
| 09 | 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 |
Table 3: Ungrouped Frequency Distribution Table
The ungrouped frequency distribution table calculates the frequency of each data singularly. Also, the frequency must be equal to the total number of observations noted after tallying.
Although the blog covers the basics of frequency distribution tables and tallying, it is okay if you still find it challenging to solve mathematical problems based on the topic. In that case, you can opt for online statistics homework help and see how the writers solve the problems. You can also get help from your professors as and when required whether It is Grouped, Ungrouped or Cumulative frequency distribution. All the best!
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