Introduction to Table Charts and Solved Examples | Data Interpretation for UGC NET PDF Download

What is Tabulation?

Tabulation of data in statistics as well as mathematics is a method of storing classified data in a tabular form. It may be complex, double, or simple, depending upon the type of categorization.

The purpose of a tabulation chart/data is to display a large volume of complex information in a systematic fashion that would enable the viewers to draw reasonable outcomes and interpretations from them.

Parts of Table in Tabulation

In order to tabulate data accurately and precisely, one must understand some of the essential parts of a table which are as follows:

• Table Number: This is the first section of a table and is presented on top of any table to facilitate straightforward identification and for further reference.
• Title of the Table: One of the most related parts of any given table is its title. The title of the table describes its contents. It is important that the title should be short and crisp and exactly worded to define the table’s contents efficiently.
• Column Headings or Captions: Captions are the piece of information on the table which is at the top of each column that tells the figures under each column.
• Row Headings: The title of every horizontal row comes under the row heading.
• Body of a Table: This is the part that includes the numeric information collected from examined facts. The data in the body is displayed in rows which are read horizontally starting from left to right and the data in the columns are read vertically from top to bottom.

Types of Tabulation

Tabulation can be classified into the following types:

Simple Tabulation or One-way Tabulation

When the data are tabulated to one aspect, it is declared to be a simple tabulation or one-way tabulation.
For example, the tabulation of data on the population of the earth divided by one feature like language is an example of a simple tabulation.

Double Tabulation or Two-way Tabulation

When the given data are tabulated according to two characters at a time, it is stated to be a double tabulation or a two-way tabulation.
For example, suppose that a table has to show the highest population in various states of India. This can be achieved by a one-way table. However, if the population has to be analyzed in terms of the total number of males and females in every state, it will ask for a two-way table.

Three-way Tabulation

Similar to the above-mentioned category, three-way charts show information handled from three mutually dependent and interrelated subjects.
Let us consider the same above example and elaborate on that further with the added category in the table. Now we need the position of literacy amongst the male and female populations in each state. The tabulation for such categories has to be placed down in a three-way table.

Complex Tabulation

When the data are tabulated according to various characteristics, it is stated to be a complex tabulation.
For example tabulation of data on the population of the planet is divided into three or more characteristics like religion, language, literacy, gender etc. is an example of a complex tabulation.

Objectives of Tabulation

Objectives of tabulation essentially connect the gap between the group of data and help analyze them. The primary objectives of tabulated data along with the uses of tabulation are discussed below:

• To Simplify Complex Data: Data or information presented in such a format decreases the bulk of information, i.e., it lessens raw data in a more simplified and exact form that can be easily interpreted by a common person in less time.
• To Highlight Important Information: Representing any data in rows and columns extends the scope to highlight the relevant information by presenting facts clearly and precisely without textual information. Thus this automatically contains any crucial data without difficulty.
• To Enable Easy Comparison: When data is displayed in an orderly manner in rows and columns, it becomes more obvious to perform the comparison of quantity on the grounds of several parameters. For example, it becomes more straightforward to determine the month when a country has experienced the highest amount of rainfall if the information is presented in a table. Otherwise, there is always room for making an error in processing the data correctly.
• To Facilitate Statistical Analysis: Tables serve as the most reliable source of classified data for statistical analysis. The task of computing percentage, distribution, correlation, etc., becomes more manageable if data is presented in the form of a table.
• To Save Space: A table presents facts in a more reliable way than the textual structure. Hence, it saves space without losing the quality and quantity of data.

An example of proper tabulation of data:
Below a table is shown to depict the total number of boys and girls in grades I, II and III in PQR School.
Table Number – 1
Gender-Wise Division of Students in Classes- I, II and III of PQR School.

Such a classification of data and tabulation of data helps estimate and mathematical analysis and propagates easy judgment-making.

How is Data in Tabulation Executed?

Tabulation of data can be carried out manually or with the aid of a computer. Frequently, the achievement of data tabulation depends on the cost, kind and scope of the study and such factors.

If tabulation is conducted out on a computer, the answers are saved in numeric form. However in the case of tabulation by hand, one can use lists, tally, card sort and count methods. The methods are explained as follows:

Tabulation of data through Direct Tally Method: In this method, the codes are initially written down in tally sheets. Then a stroke is marked on codes to denote the answer. After each fourth stroke code, the fifth response is presented by putting a horizontal or diagonal line within the stroke.

Tabulation of data through Card Sort and Count Method: This is possibly the most effective hand tabulation method where the data is entered in cards of various dimensions and shapes with the help of a set of holes. Following the cards belonging to the individual categories are separated and counted, and their frequency is entered.

Tabulation of data through List and Tally Method: In this method, a large number of applications are listed in one sheet. The answers to each question are then inserted into rows, and the code corresponding to a specific question is outlined in columns.

Rules of Tabulation

There are some general rules of tabulation discussed below that must be followed while creating tables.

• The tables represented should be self-explanatory. Moreover, footnotes form a portion of tables, they should not be necessary to define the meaning of the data displayed in a table.
• If the amount of information is valuable, it is best to place them on multiple tables rather than a single one.
• However, each table design should also be complete in itself and must serve the goal of the analysis.
• The figure of rows and columns should be kept minimum to present data in a brief and concise manner.
• Before the actual tabulation, data should be approximated, wherever required.
• Stubs and titles should be self-explanatory and need not require the assistance of footnotes to be comprehended.
• If certain conditions of data gathered cannot be tabulated under any stub or captions, they should be placed in a separate table with the heading of miscellaneous.
• Quantity and quality of data should never be negotiated under any situation while creating a table.

Solved Example

Example 1: The following table gives the sales of batteries manufactured by a company over the years. Study the table and answer the questions that follow:
(i) The total sales of all the seven years is the maximum for which battery ?
(a) 4AH
(b) 7AH
(c) 32AH
(d) 35AH
Ans: (c)
The total sales (in thousands) of all the seven years for various batteries are:
For 4AH = 75 + 90 + 96 + 105 + 90 + 105 + 115 = 676
For 7AH = 144 + 126 + 114 + 90 + 75 + 60 + 85 = 694
For 32AH = 114 + 102 + 75 + 150 + 135 + 165 + 160 = 901
For 35 AH= 102 + 84 + 105 + 90 + 75 + 45 + 100 = 601
For 55 AH= 108 + 126 + 135 + 75 + 90 + 120 + 145 = 799.
Clearly, sales are maximum in case of 32AH batteries.

(ii) What is the difference in the number of 35AH batteries sold in 1993 and 1997 ?
(a) 24000
(b) 28000
(c) 35000
(d) 39000
Ans: (d)
Required difference = [(84 - 45) x 1000] = 39000. 

(iii) The percentage of 4AH batteries sold to the total number of batteries sold was maximum in the year:
(a) 1994
(b) 1995
(c) 1996
(d) 1997
Ans: (d)
The percentages of sales of 4AH batteries to the total sales in different years are:
For 1992=(75*100/543)%=13.81%
For 1993=(90*100)/528%=17.05%
For 1994=(96*100/525)%=18.29%
For 1995=(105*100/510)%=20.59%
For 1996=(90*100/465)%=19.35%
For 1997=(105*100/495)%=21.21%
For 1998=(115*100/605)%=19.01%
Clearly, the percentage is maximum in 1997. 

(iv) In the case of which battery there was a continuous decrease in sales from 1992 to 1997 ?
(a) 4AH
(b) 7 AH
(c) 32AH
(d) 35AH
Ans: (b)
From the table it is clear that the sales of 7AH batteries have been decreasing continuously from 1992 to 1997. 

(v) What was the approximate percentage increase in the sales of 55AH batteries in 1998 compared to that in 1992 ?
(a) 28%
(b) 31%
(c) 33%
(d) 34%
Ans: (d)
Required Percentage =(145- 108)/108)*100 %=34.26%=34%.

Example 2: The following table gives the percentage of marks obtained by seven students in six different subjects in an examination. Study the table and answer the questions based on it. The numbers in the brackets give the maximum marks in each subject.
(i) What was the aggregate of marks obtained by Sajal in all the six subjects?
(a) 409
(b) 419
(c) 429
(d) 449
Ans: (d)
Aggregate marks obtained by Sajal = [(90% of 150) + (60% of 130) + (70% of 120) + (70% of 100) + (90% of 60) + (70% of 40)] = 135 + 78 + 84 + 70 + 54 + 28 = 449. 

(ii) What is the overall percentage of Thrun?
(a) 52.5%
 (b) 55%
(c) 60%
(d) 63%
Ans: (c)
Aggregate marks obtained by Thrun = [(65% of 150) + (35% of 130) + (50% of 120) + (77% of 100) + (80% of 60) + (80% of 40)] = 97.5 + 45.5 + 60 + 77 + 48 + 32 = 360.

Total maximum marks (of all the six subjects)

= (150 + 130 + 120 + 100 + 60 + 40) = 600.

(iii) What are the average marks obtained by all the seven students in Physics? (rounded off to two digits after decimal) 
(a) 77.26 
(b) 89.14
(c) 91.37 
(d) 96.11
Ans: (b)
Average marks obtained in Physics by all the seven students
= 1/7 [(90% of 120) + (80% of 120) + (70% of 120) + (80% of 120) + (85% of 120) + (65% of 120) + (50% of 120)]
= 1/7 [(90 + 80 + 70 +80 + 85 + 65 + 50)% of 120]
= 1/7 [520% of 120] = 89.14.

(iv) The number of students who obtained 60% and above marks in all the subjects is :
(a) 1
(b) 2
(c) 3
(d) None of these
Ans: (b)
From the table it is clear that Sajal and Rohit have 60% or more marks in each of the six subjects. 

(v) In which subject is the overall percentage the best?
(a) History
(b) Maths
(c) Physics
(d) Chemistry
Ans: (b)
We shall find the overall percentage (for all the seven students) with respect to each subject. The overall percentage for any subject is equal to the average of percentages obtained by all the seven students since the maximum marks for any subject is the same for all the students.
Therefore, overall percentage for:


Clearly; this percentage is highest for Maths.

Example 3: Study the following table carefully and answer these questions:

(i) Combining the states P and Q, together in 1998, what is the percentage of the candidates qualified to that of the candidates appeared?
(a) 10.87%
(b) 11.49%
(c) 12.35%
(d) 12.54%
Ans: (c)

(ii) The percentage of the total number of qualified candidates to the total number appeared candidates among all the five states in 1999 is : (a) 11.49%
(b) 11.84%
(c) 12.21%
(d) 12.57%
Ans: (b)
Required Percentage

(iii) What is the percentage of candidates qualified from State N for all the years together, over the candidates appeared from State N during all the years together?
(a) 12.36%
(b) 12.16%
(c) 11.47%
(d) 11.15%
Ans: (d)
Required Percentage
=[(840+1050+920+980+1020)/(7500+9200+8450+9200+8800)]*100%
=(4810*100)/43150]
=11.15%

(iv) What is the average of candidates who appeared from State Q during the given yeas?
(a) 8700
(b) 8760
(c) 8810
(d) 8990
Ans: (d)
Required average
=(8100+9500+8700+9700+8950)/5
=44950/5
=8990

(v) In which of the given years the number of candidates appeared from State P has maximum percentage of qualified candidates?
(a) 1997
(b) 1998
(c) 1999
(d) 2001
Ans: (d)
 The percentages of candidates qualified to candidates appeared from State P during different years are:


∴ Maximum percentage is for the year 2001. 

(vi) Total number of candidates qualified from all the states together in 1997 is approximately what percentage of the total number of candidates qualified from all the states together in 1998 ?
(a) 72%
(b) 77%
(c) 80%
(d) 83%
Ans: (c)
Required Percentage

Example 4: Study the following table carefully and answer tbe questions given below:
(i) The number of students scoring less than 40% marks in aggregate is :
(a) 13
(b) 19
(c) 20
(d) 27
Ans: (d)
We have 40% of 50
∴ Required number = Number of students scoring less than 20 marks in aggregate = 100 - number of students scoring 20 and above marks in aggregate = 100 - 73 = 27.

(ii) If at least 60% marks in Physics are required for pursuing higher studies in Physics,how many students will be eligible to pursue higher studies in Physics?
(a) 27
(b) 32
(c) 34
(d) 41
Ans: (b)
We have 60% of 50
∴ Required number = Number of students scoring 30 and above mark in Physics = 32.

(iii) What is the difference between the number of students passed with 30 as cut- off marks in Chemistry and those passed with :JUas cut- off marks in aggregate?
(a) 3
(b) 4
(c) 5
(d) 6
Ans: (d)
Required difference = (Number of students scoring 30 and above in mark in Chemistry) (Number of students scoring 30 and above marks in aggregate) = 27 – 21 = 6. 

(iv) The percentage of the number of students getting at least 60% marks in Chemistry over those getting at least 40% marks in aggregate, is approximately:
(a) 21%
(b) 27%
(c) 29%
(d) 31%
Ans: (c)
Number of students getting at least 60% marks in Chemistry
= Number of students getting 30 and above marks in Chemistry = 21.
Number of students getting at least 40% marks in aggregate
= Number of students getting 20 and above marks in aggregate = 73.

(v) If it is known that at least 23 students were eligible for a Symposium on Chemistry the minimum qualifying marks in Chemistry for eligibility to Symposium would lie in the range:
(a) 40- 50
(b) 30- 40
(c) 20-30
(d) Below 20
Ans: (c)
Since 66 students get 20 and above marks in Chemistry and out of these 21 students get 30 and above marks, therefore to select top 35 students in Chemistry, the qualifying marks should lie in the range 20- 30.