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Does your heart skip a beat when you come across the word mathematics? Do you find yourself comfortable with statistics and frequency distribution tables?
Probably, you might not have insight into the most efficient way of handling frequency distribution table-related problems. If that is the case, then this blog will provide you with comprehensive guidance and the necessary steps to deal with the questions.
But, first, you need to comprehend the concept of frequency distribution tables.
When the concept is a bit intricate to grasp, the first thing you need is to dissect the term and understand the meaning of individual words. The term frequency in frequency distribution table refers to the number of times an event is occurring in a particular sample space. For instance, if you refer to the frequency of observation, it signifies the number of times the observation takes place in the specific data.
The frequency of 1 in {1,2,1,3,5,6,6,1} is 3.
The frequency distribution tables deal with either categorical variables or quantitative variables. If the quantitative variables refer to the numbers, the categorical or qualitative variables refer to a brand, colour of eye etc.
Frequency distribution table provides a detailed visual representation of a data which allows the analyst to search for a pattern.
There are various ways by which a frequency distribution table can be prepared. Let’s delve deep into the subject matter to gain more information.
Tally Marks
Tally marks are one of the most effective ways of constructing a frequency distribution table. For instance, you conduct a survey on the number of households having an aquarium. The outcome is noted as 3, 0, 1, 4, 4, 1, 2, 0, 2, 2, 0, 2, 0, 1, 3, 1, 2, 1, 1, 3. It might seem like a string of meaningless data. But, the frequency distribution table in the form of tally marks helps to distinguish the data and make it more relevant.
| Number of aquariums | Tally | Frequency |
| 0 | III | 4 |
| 1 | IIII I | 6 |
| 2 | IIII | 5 |
| 3 | III | 3 |
| 4 | II | 2 |
Table 1: Frequency Distribution Table of Number of Aquariums (using Tally marks)
Here the category is the number of aquariums. The final column represents the frequency of the number of aquariums present in each household. For instance, the number of aquariums in most of the house surveyed was found to be six. Thus, it has been written against the category.
Now that we know about one procedure for estimating the frequency, we’ll take a look at another method for preparing frequency distribution table.
Accurate organization of the various data in the form of frequency distribution tables can be understood through the following example.
For instance, let us assume that a test has been conducted in the classroom and the results (out of 200) are 118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, and 154. However, the information does not reveal much, and it can be best understood through a frequency distribution table. The steps have been discussed in details.
The steps that are required to prepare the frequency distribution table have been provided below.
1. You have to choose the class
Here you need to decide the number of classes involved in the data. The above example will help you comprehend the fact.
For the test results mentioned above, we are selecting five classes between five and twenty classes. However, you have to include a few items in each category. Now you might choose five classes inserting four items per category and not involve twenty classes.
2. Minimum and maximum value
2. A)
Following the choice of the class, you need to sort the data
Here a subtraction is required (the difference between the minimum and maximum data).
For instance, the maximum value in the test result is 154, and the minimum value is 118.
154-118=36.
2. B)
Next, to prepare the frequency distribution tables, divide 36 by the number of classes chosen, that is, 5.
36/5= 7.2
2. C)
To achieve the class width, you have to round up the result 7.2 to 8.
2. D)
To write the first minimum data value, write the lowest result 118.
To get the next lower class limit, add the class width and the minimum data value,
118+8= 126.
2. F)
The previous step has to be repeated for the other minimum data values until it is equivalent to the number of classes chosen initially at the beginning of the frequency distribution table.
Thus, the five minimum data values are
118
126 (118+8)
134 (126+8)
142 (134+8)
150 (142+8)
2. G)
Once you are through with the minimum data values, it is time to write the upper-class limits.
What does it signify? It means that these are the highest values present in the category. In most cases, you have to subtract one from the class width and add it to the minimum data value.
So, you have
118+(8-1)=125
118-125
126-133
134-141
142-149
150-157
3. Completing the table
Once the entire second step has been completed, you need to complete the frequency distribution tables.
First, you have to prepare the table with appropriate headings and labelling of the columns. Following this, you have to calculate the number of items in each class and write the corresponding total in the second column.
Thus. You will have.
| TEST RESULTS | NUMBER |
| 118-125 | 4 |
| 126-133 | 6 |
| 134-141 | 3 |
| 142-149 | 2 |
| 150-157 | 2 |
Table 2: Frequency Distribution Table on the Test Results
This will conclude the entire frequency distribution table preparation process.
However, you might also come across terminologies involving grouped and ungrouped data.
The essence is literal. In the grouped data, you get an organized display of the data by aggregation of individual observations of variables in a group. On the other hand, ungrouped information is not assembled correctly.
Now, if you are still struggling with the conceptual aspect of the frequency distribution tables, you should seek professional assistance. You might ask your friend or teachers to help you out with the intricate details.
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