Every day we come across a lot of information in facts, numerical values, tables, graphs, etc. These are provided by newspapers, televisions, magazines, and other means of communication. These may relate to cricket batting or bowling averages, profits of a company, temperatures of cities, expenditures in various sectors of a five-year strategy, polling results, and so on. These facts or figures, which are numerical or otherwise, collected with a definite purpose are called data.

Large volumes of data may be easily summarized in statistical tables of means, counts, standard deviations, etc. We may use categorical group variables to calculate data for specific groups. The tables are comparable in structure to those produced by cross-tabulation. The tables which display sets of data across rows and columns are called data tables.

Data Table: Definition

If the number of observations is huge, then organizing data in ascending or descending or serial order is a tedious job. The directive does not tell us much except maybe the minimum (s) and maximum(s) of data. So, to make it easy to understand and clear, we can tabulate data in the form of a table; this table is called a data table.

Data Tables Representation

After collecting data, the investigator must find ways to condense them in tabular form to study their salient features. Such an arrangement is called the representation of data.

i) Serial order of alphabetic order
ii) Ascending order
iii) Descending order

The raw data, when put in ascending or descending order of magnitude, is called an array.
The raw data is called an array or array data when placed in ascending or descending order of magnitude.
The collected data is arranged in rows and columns in a table called a data table.
For example, let the marks obtained by \(30\) students of class in a class test, out of  marks, according to their roll numbers, be: \(39,25,5,33,19,21,12,41,12,21,19,1,10,8,12,17,19,17,17,41,40,12,41,33,\)
\(19,21,33,5,1,21.\)

In the very first column of the table, we write all marks from lowest to highest. We now look at the first value on the given raw data and put a vertical line in the second column parallel to it. We see the second value in the given raw data and put a bar opposite it in the second column. This process is repeated till all observations in the given raw data are exhausted.

The bars drawn in the second column are known as tally marks, and to facilitate, we record tally marks in bunches of five; the fifth tally mark is drawn diagonally across the first four. We eventually count the number of tally marks corresponding to each observation and write in the third column.         

Marks	Tally Marks	No. of students
\(1\)	\(||\)	\(2\)
\(5\)	\(||\)	\(2\)
\(8\)	\(|\)	\(1\)
\(10\)	\(|\)	\(1\)
\(12\)	\(||||\)	\(4\)
\(17\)	\(|||\)	\(3\)
\(19\)	\(||||\)	\(4\)
\(21\)	\(||||\)	\(4\)
\(25\)	\(|\)	\(1\)
\(33\)	\(|||\)	\(3\)
\(39\)	\(|\)	\(1\)
\(40\)	\(|\)	\(1\)

This way of presentation of data is known as frequency distribution. Marks are called variates, and the number of students who have secured a particular number of marks is called the frequency of the variate. The number of times an observation occurs in the given data is called the frequency of the observation.

Data Table: Types

We can classify statistical tables in accordance with the two major categories, namely, general tables and summary tables.

1. General tables contain a compilation of detailed information, including all that is relevant to the subject or theme. The primary purpose of such tables is to present all the information available on a specific problem in one place for easy reference. They are typically placed in the postscripts of reports.
2. Summary tables are specifically designed to serve some specific purposes. They are smaller in size than available tables, with an emphasis on some aspects of data and are usually contained within the text. The summary tables are also called derived tables because they are derived from the available tables. Information that is contained in the summary table seeks at assessment and inference. Hence, they are also known as explanatory tables.

We may further classify the statistical tables into two broad classes, namely simple tables, and complex tables. A simple table provides summary information on a single characteristic and is also called a univariate table.

The marks obtained by a batch of students in a class test are displayed here:

Marks	Number of Students
\(0 – 10\)	\(10\)
\(10 – 20\)	\(12\)
\(20 – 30\)	\(17\)
\(30 – 40\)	\(20\)
\(40 – 50\)	\(15\)
\(50 – 60\)	\(6\)

This table is based upon a single attribute, namely marks, and from this table, one may see the number of students in each class of marks.

A complex table contains information about comprehensive information and presents them into two or more interrelated categories. For example, if there are two coordinate factors, the table is called a two-way table or bi-variate table; if the number of coordinate groups is three, it is a case of three-way tabulation. Similarly, if it is based on more than three coordinate groups, the table is known as higher-order tabulation or a manifold tabulation.

Below is a two-way table, in which there are two characteristics, namely, marks secured by the students in the test and the gender of the students.

Data Table vs Frequency Table

Data Table: A data table combines data organized into rows and columns, and each table must have a name.

Frequency Table: A frequency table is constructed by arranging collected data values in ascending or descending order of magnitude with their corresponding frequencies.

Uses of Data Table

1. In statistics, the data are the individual pieces of information recorded, and it is used for the analysis process.
2. Tables are used to arrange the data that is too comprehensive or complex to be described sufficiently in the text, allowing the reader to see the results quickly. They can highlight trends or patterns in the data and make a manuscript more readable by removing numeric data from the text.

Solved examples – Data Table

Q.1. Given below is the data that show the number of children in \(20\) families of a colony: \(2,1,3,1,2,1,1,3,2,3,2,3,2,2,4,3,1,4,3,2.\) Organize the above data in ascending order and then put it in tabular form.
Ans: Arranging the data in ascending order, we get the given data as \(1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4.\) For counting purposes, we use tally marks. After putting \(4\) tally marks vertically, we put across as shown below and we then take the tally marks in the same manner, counting in sets of fives.
Now, we may prepare the frequency table, as shown below.

Q.2. Given below are the heights (in \({\text{cm}}\)) of some students in class \(6\):

\(144\)	\(143\)	\(148\)	\(134\)	\(146\)	\(156\)	\(139\)	\(147\)	\(148\)	\(135\)
\(136\)	\(132\)	\(150\)	\(136\)	\(148\)	\(142\)	\(159\)	\(149\)	\(135\)	\(139\)
\(146\)	\(159\)	\(142\)	\(149\)	\(145\)	\(149\)	\(129\)	\(149\)	\(139\)	\(148\)
\(145\)	\(142\)	\(151\)	\(142\)	\(146\)	\(152\)	\(134\)	\(141\)	\(137\)	\(136\)
\(157\)	\(152\)	\(148\)	\(133\)	\(148\)	\(146\)	\(148\)	\(153\)	\(139\)	\(131\)
\(136\)	\(137\)	\(149\)	\(142\)	\(153\)	\(152\)	\(152\)	\(141\)	\(148\)	\(153\)
\(148\)	\(143\)	\(142\)	\(149\)	\(149\)	\(162\)	\(154\)	\(149\)	\(142\)	\(152\)
\(149\)	\(137\)

Q3. Arrange the data and form a frequency distribution table.

Ans: We will make groups such as \(125 – 130,130 – 135,\) etc., which are called classes or class intervals. In the interval \(125 – 130,125\) is called the lower-class limit, and \(130\) is called the upper-class limit. The difference between the upper-class limit and lower-class limit is called the size or width of the class width is \(5.\)
In the table, a number such as \(135\) would fall in two classes, viz. \(130 – 135\) and \(135 – 140.\) However, by convention, \(135\) is included in classes \(135 – 140.\) Similarly, a number like \(150\) would fall in class \(150 – 155.\)

Q.4. The temperatures of some cities on a specific day are given in the table below. Answer the questions based on the data.

City	Maximum	Minimum
Bengaluru	\({26^ \circ }\,{\text{C}}\)	\({20^ \circ }\,{\text{C}}\)
Chennai	\({36^ \circ }\,{\text{C}}\)	\({26^ \circ }\,{\text{C}}\)
Delhi	\({40^ \circ }\,{\text{C}}\)	\({28^ \circ }\,{\text{C}}\)
Kolkata	\({36^ \circ }\,{\text{C}}\)	\({25^ \circ }\,{\text{C}}\)
Mumbai	\({33^ \circ }\,{\text{C}}\)	\({25^ \circ }\,{\text{C}}\)

a) Which city was the hottest on that day?
b) Which city was the coolest on that day?

Ans: (a) City Delhi was the hottest on that day.
(b) City Bengaluru was the coolest on that day.

Q.5. The weights (in \({\text{Kg}}\)) of \(38\) students of class \({\text{VII}}\) of a specific school are given below: \(36,38,42,46,37,49,51,53,44,37,41,46,44,33,32,40,42,41,39,50,33,38,42\)
\(47,49,34,34,38,42,43,35,43,44,48,42,37,44.\) Construct a grouped frequency distribution table.
Ans: Here, maximum value \( = 53\) and minimum value \( = 32\)
Therefore, range \( = 53 – 32 = 21\)
Let us form \(5\) classes each of size \(5.\)
Since we want to include \(53\) in the last class, \(55\) can be taken as the upper limit of the last class.
Hence, we can take the classes as \(30 – 35,35 – 40,40 – 45,45 – 50,50 – 55.\)
The grouped frequency distribution table for the given data is:

 

Q.6. Given below is a frequency distribution table. Read it and answer the questions that follow:

Class interval	Frequency
\(10 – 20\)	\(8\)
\(20 – 30\)	\(10\)
\(30 – 40\)	\(12\)
\(40 – 50\)	\(18\)
\(50 – 60\)	\(10\)
\(60 – 70\)	\(5\)
\(70 – 80\)	\(7\)
Total	\(70\)

a) Which interval has the highest frequency?
b) Which interval has the lowest frequency?
c) Which two classes have the same frequency?
d) What is the lower limit of second-class interval?

Ans: a)Class interval \(40 – 50\) has the highest frequency \(\left({18} \right).\)
b) Class interval \(60 – 70\) has the lowest frequency \(\left({5} \right).\)
c) Classes \(20 – 30\) and \(50 – 60\) have the same frequency \(\left({10} \right)\) each.
d) The lower limit of second-class interval \(20 – 30\) is \(\left({20} \right).\)

Summary

In this article, we learnt about definition data table, data tables representation, types of data table, data table V/s frequency table, uses of data table, solved examples on data table, FAQs on data table.
This article’s learning outcome is that using a data table, we can record extensive data in such a way that the data can be easily written, read, and interpreted.

Frequently Asked Questions – Data Table

Frequently asked questions related to data table is listed as follows:

Q.1. What is meant by data?
Ans: The collection of information in the form of numerical figures is known as data.

Q.2. What are the uses of data table?
Ans: 1. In Statistics, the data are the individual pieces of information recorded, and it is used for the analysis process.
2. Tables are used to organize data that is too detailed or complicated to be described adequately in the text, allowing the reader to see the results quickly. They can highlight trends or patterns in the data and make a manuscript more readable by removing numeric data from the text.

Q.3. What is raw data?
Ans: The word data means information is the collection of observations in the first step in statistical investigations. The numerical observations collected by an observer cannot be put to any use immediately and directly. That is why it is called raw data.

Q.4. How to find mean using data tables?
Ans: If a variate \(X\) takes values \({x_1},{x_2}, \ldots ,{x_n}\) with corresponding frequencies \({f_1},{f_2},{f_3}, \ldots ,{f_n}\) respectively, the mean of these values is given by \(\bar X = \frac{{{f_1}{x_1} + {f_2}{x_2} + \cdots + {f_n}{x_n}}}{{{f_1} + {f_2} + \cdots + {f_n}}}\)

Q.5. What is the class size in data tables?
Ans: Class size in data tables is the difference between class limits.
That is the class \( – \)size\( = \) upper class limit \( – \) lower class limit.