Tabulation of Data
Once the raw data is collected, it needs to be summarized and presented to the decision-maker in a form that is easy to comprehend. The manager must be able to look at the data so as to decide what further analysis is required. Tabulation helps this process through the effective presentation.
Tabulation not only condenses the data but also makes it easy to understand. Tabulation is the fastest way to extract information from the mass of data and is hence popular even among those not exposed to the statistical method. The report card of a school is the most common example.
Table of Contents
Objectives of Tabulation
The main objectives of tabulation are:
- To simplify complex data.
- To highlight the chief characteristics of the data.
- To clarify the objective of the investigation.
- To present data in a minimum space.
- To detect errors and omissions in the data.
- To facilitate comparison of data.
- To facilitate reference.
- To identify trends and tendencies of the given data.
- To facilitate statistical analysis.
Main Parts of a Table
The main parts of the table are given below:
- Table Number: This number is helpful in the identification of a table. This is often indicated at the top of the table.
- Title: Each table should have a title to indicate the scope, and nature of contents of the table in an unambiguous and concise form.
- Captions and stubs: A table is made up of rows and columns. Headings or subheadings used to designate columns are called captions while those used to designate rows are called stubs.
A caption or a stub should be self-explanatory. A provision of totals of each row or column should always be made in every table by providing an additional column or row respectively. - Main Body of the Table: This is the most important part of the table as it contains numerical information. The size and shape of the main body should be planned in view of the nature of the figures and the objective of the investigation.
The arrangement of numerical data in the main body is done from top to bottom in columns and from left to right in rows. - Ruling and Spacing: Proper ruling and spacing are very important in the construction of a table. Vertical lines are drawn to separate various columns with the exception of the sides of a table.
Horizontal lines are normally not drawn in the body of a table; however, the totals are always separated from the main body by horizontal lines. Further, the horizontal lines are drawn at the top and the bottom of a table.
Spacing of various horizontal and vertical lines should be done depending on the available space. Major and minor items should be given space according to their relative importance. - Head-note: A head-note is often given below the title of a table to indicate the units of measurement of the data. This is often enclosed in brackets.
- Footnote: Abbreviations, if any, used in the table or some other explanatory notes are given just below the last horizontal line in the form of footnotes.
- Source note: This note is often required when secondary data are being tabulated. This note indicates the source from where the information has been obtained. The source note is also given as a footnote.
Example: The main parts of a table can also be understood by looking at its broad structure given below:
Structure of a Table
Table No: ………….
Title: …………………
Foot Note:
Source:
Rules for Tabulation
Now, let us learn about the general rules of tabulation.
- The table should be simple and compact and contain simple details.
- Tabulation should be in accordance with the objective of the investigation.
- The unit of measurement must always be indicated in the table.
- The captions and stubs must be arranged in a systematic manner so that it is easy to grasp the table.
- A table should be complete and self-explanatory.
- As far as possible the interpretative figures like totals, ratios, and percentages must also be provided in a table.
- The entries in a table should be accurate.
- The table should be attractive to draw the attention of readers.
Types of Tabulation
Statistical tables can be classified into various categories depending on the basis of their classification. Broadly speaking, the basis of classification can be any of the following:
- Purpose of investigation
- Nature of presented figures
- Construction
Different types of tables, thus, obtained are shown in the following chart.
- Classification on the Basis of Purpose of Investigation
- Classification on the Basis of the Nature of Presented Figures
- Classification on the Basis of Construction
- One-way Tabulation
- Two-way Tabulation
- Multi-way Tabulation
- Advantages of Tabulation
Classification on the Basis of Purpose of Investigation
These tables are of two types viz. General purpose table and Special purpose table.
- General purpose table: A general purpose table is also called as a reference table. This table facilitates easy reference to the collected data. In the words of Croxton and Cowden, “The primary and usually the sole purpose of a reference table is to present the data in such a manner that the individual items may be readily found by a reader.”
A general purpose table is formed without any specific objective but can be used for a number of specific purposes. Such a table usually contains a large mass of data and is generally given in the appendix of a report.
An example of a general-purpose table is as follows:
| Position | Description | Values |
|---|---|---|
| 1 | Type | LOG (or L) – Log FNC (or F) – Fence GRF (or G) – Graph GTB (or T) – Graphical Table GTD (or X) – Graphical Text Document HST (or H) – Histogram TTB (or A) – Text Table TXD (or D) – Text Document SMP – Site Map |
| 2 | Paper Size | A – US Letter 4 – ISO A4 B – US 11×17 3 – ISO A3 L – US Legal |
| 3 | Content | G – Predominantly Geotechnical E – Predominantly Environmental R – Predominantly Rock Core N – Not Applicable or can be generally used |
| 4 | Well | W – Has well (applies to logs & fences) N – No well or Not Applicable |
| 5 | Graph | G – Has graph (applies to logs & fences) N – No graph or Not Applicable |
| 6 | Legend | L – Has legend N – No legend or Not applicable |
- Special purpose table: A special purpose table is also called a text table or a summary table or an analytical table. Such a table presents data relating to a specific problem.
According to H. Secrist, “These tables are those in which are recorded, not the detailed data which have been analyzed, but rather the results of the analysis.”
Such tables are usually of smaller size than the size of reference tables and are generally found to highlight relationships between various characteristics or to facilitate their comparisons.
Classification on the Basis of the Nature of Presented Figures
Tables, when classified on the basis of the nature of presented figures can be Primary tables and Derivative tables.
- Primary Table: Primary table is also known as the original table and it contains data in the form in which it was originally collected.
- Derivative Table: A table that presents figures like totals, averages, percentages, ratios, coefficients, etc., derived from original data. A table of time series data is an original table but a table of trend values computed from the time series data is known as a derivative table.
Classification on the Basis of Construction
Tables, when classified on the basis of construction, can be Simple tables, Complex tables, and Cross-classified tables.
- Simple Table: In this table, the data are presented according to one characteristic only. This is the simplest form of a table and is also known as a table of the first order.
Example: The following blank table, for showing the number of workers in each shift of a company, is an example of a simple table.
| Shifts | No. of Workers |
|---|---|
| | | |
| || | |
| ||| | |
| Total |
- Complex Table: A complex table is used to present data according to two or more characteristics. Such a table can be two-way, three-way, multi-way, etc.
- Two-way Table: Such a table presents data that is classified according to two characteristics. In such a table the columns of a table are further divided into sub-columns.
Example: The example of such a table is given below
- Two-way Table: Such a table presents data that is classified according to two characteristics. In such a table the columns of a table are further divided into sub-columns.
| Shifts | Males | No. of Workers | Females | Total |
|---|---|---|---|---|
| | | ||||
| || | ||||
| ||| | ||||
| Total |
- Three-way Table: When three characteristics of data are shown simultaneously, we get a three-way table as shown below in the example.
Example: - Multi-way Table: If each shift is further classified into three departments, say, manufacturing, packing, and transportation, we shall get a four-way table, etc. 9911740271
- Cross-classified Table: Tables that classify entries in both directions, i.e., row-wise and column-wise, are called cross-classified tables. The two ways of classification are such that each category of one classification can occur with any category of the other.
The cross-classified tables can also be constructed for more than two characteristics also. A cross-classification can also be used for analytical purposes, e.g., it is possible to make certain comparisons while keeping the effect of other factors constant.
Example: Draw a blank table to show the population of a city according to age, sex, and unemployment in various years.
Example: In a sample study about coffee habit in two towns; the following information were received:
Town A: Females were 40%; total coffee drinkers were 45%; and male non-coffee drinkers were 20%.
Town B: Males were 55%; male non-coffee drinkers were 30%; and female coffee drinkers were 15%.
Represent the above data in a tabular form.
Solution: The figures are in percentage
| Habit | Males | Females | Total | Males | Females | Total |
|---|---|---|---|---|---|---|
| Coffee Drinkers | 40 | 5 | 45 | 25 | 15 | 40 |
| Non-coffee Drinkers | 20 | 35 | 55 | 30 | 30 | 60 |
| Total | 60 | 40 | 100 | 55 | 45 | 100 |
One-way Tabulation
Tabulation is primarily counting how many observations are in a particular category. Tabulation is like an in-process inventory. Tabulation in itself may not be the end of statistical processing. It may be noted that once we tabulate the data, we usually do not go back to the raw data.
Any improper tabulation would definitely mislead the decision-maker for further processing. Hence, before tabulation manager must give sufficient thought to decide what kind of tabulation is required for decision-making.
We need to first decide on characteristics, their values and ranges, the title of the table, stubs for the rows, headings for the columns, scale, and dimensions used, footnotes, pivots if we need them, etc. The table must suit the purpose for which the data is being processed.
We also need to decide on the size of the table, clarity, approximations, boundaries, appearance, order, readability, etc. A meaningful title not only helps the manager to focus on the purpose, and thus, group the data properly but also others who refer to the table later.
The next step is to decide on appropriate column headings; row stubs units and dimensions of the quantities used, labels for summary figures, etc. to improve the readability of the table. Many times the requirement of statistical analysis is to count the frequency of the distinct value of a variable.
When we arrange the range of values (or just values) and their frequencies the tabulation is known as one way. The variable could be either quantitative or normative.
For example, the examination result of an MBA could be tabulated as,
| Class | Number of Students (Frequency f) |
|---|---|
| Distinction (≥75%) | 26 |
| First Class (60-75%) | 72 |
| Second Class (50-60%) | 94 |
| Pass Class (40-50%) | 42 |
| Fail | 16 |
| Total Students Appeared | 250 |
Foot Note
- Each class includes its lower limit.
- Fail indicates failure in any one or more subjects irrespective of the percentage marks.
Example: Represent the following information in a table:
The number of students in a college in the year 1961 was 1100; of those 980 were boys and the rest were girls. In 1971 the number of boys increased by 100% and that of girls increased by 300% as compared to their strength in 1961. In 1981 the total number of students in a college was 3600, the number of boys being double the number of girls.
Solution:
| Year | Number of Boys | Number of Girls | Total Students |
|---|---|---|---|
| 1961 | 980 | 120 | 1100 |
| 1971 | 1960 | 480 | 3600 |
| 1981 | 2400 | 1200 | 2440 |
Two-way Tabulation
There are occasions when we want to summarize the frequency table against two attributes (categories) and want the count of the same population belonging to all possible combinations of these two attributes.
For example, we want to know the frequency of personnel with different combinations of salary earned category and education qualification category for a given company. Since there are two variables, we call it a two-way tabulation (also referred to as cross-tabulation).
We prepare the table with one of the categories varied along the rows and another along the columns. For counting the frequency, a pair of combinations of categories one from each direction is considered. Thus, we get a table in m × n matrix form, with each cell containing data for one combination.
This is also known as a contingency table. With m rows and n columns, we get m categories of one variable varying along the column and n categories of another variable varying along the row. There are obviously mn cells containing distinct mutually exclusive and collectively exhaustive data.
It may be noted that a two-way table can be converted to a one-way table with mn distinct values of a combination variable. This is called a normalized table or a flat table in database management.
Example: In a survey conducted in a city about the preference for Coke or Pepsi or Mazza, the sample consisted of 400 people which included 150 women and 250 men. It was observed that 50 women preferred Coke and 40 preferred Pepsi.
In the case of men, the preference was 100, 80, and 70 respectively. Present the information in the two-way table and answer the following:
- What is the percentage of men in Coke’s preferred population?
- What is the proportion of the population preferring Pepsi?
- What is the proportion of women preferring Maza in the total population?
Solution:
| Men | Woman | Total | |
|---|---|---|---|
| Coke Preferring People | 100 | 50 | 150 |
| Pepsi Preferring People | 80 | 40 | 120 |
| Maza Preferring People | 70 | 60 | 130 |
| Total | 250 | 150 | 400 |
- Percentage of men in Coke preferring population =
- Proportion of the population preferring Pepsi =
- Proportion of women preferring Maza in the total population = 0.15
Multi-way Tabulation
We can carry out cross-tabulation with more than two variables. It is called a nested table. In fact, in most of business situations, the tabulation may have more than two variables (usually 10 to 15). Up to about 3 to 4 variables could be shown on two-dimensional papers.
These can also be represented as flat tables by taking one composite variable of dimension n1 × n2 × n3 × n4 × n5 × …, where n1 , n2 , n3 , n4 , n5 …are dimensions of each variable (attribute). Obviously, the number grows so rapidly, that it becomes too voluminous and complex to get any meaningful information for decision-making.
However, that does not mean such multidimensional data is not tabulated. It is tabulated using computer databases like MS Access, FOXPRO, Oracle, etc. We cannot view it together but definitely use it for decision-making through ‘query language’.
Database management systems and query languages are beyond the scope of this book. One simple, three-dimensional, tabulation is shown in the following example.
Example: A mutual fund wants to compare the performance of shares on NSE over the past three years. It wants to categorize the shares as below average, average, and above average as compared to the benchmark. It also wants to group the shares as large-cap, mid-cap, and small-cap.
The data obtained is as follows: In 40 large-cap shares studied 27 performed average and 11 above average in the year 2004. Similarly, figures for the years 2005 and 2006 were 34 and 8 out of 50, and 32 and 16 out of 50 respectively.
In the mid-cap segment, the number of shares below average, average, and above average was 22, 35, and 23 in the year 2004. These were 17, 40, 23 for the year 2005 and 13, 38 and 29 for the year 2006 respectively.
In the case of small-cap shares the performance figures for years 2004, 2005, and 2006 in categories below average, average, and above average were 26, 32, 42; 25, 36, 39; and 12, 40, and 48 respectively. Present the data as a multi-way table.
Solution:
| Year | 2004 | 2005 | 2006 | |
|---|---|---|---|---|
| Large Cap | Below Average | 12 | 8 | 2 |
| Average | 27 | 34 | 32 | |
| Above Average | 11 | 8 | 16 | |
| Total | 50 | 40 | 40 | |
| Mid Cap | Below Average | 22 | 17 | 13 |
| Average | 35 | 40 | 38 | |
| Above Average | 23 | 23 | 29 | |
| Total | 80 | 80 | 80 | |
| Small Cap | Below Average | 26 | 25 | 12 |
| Average | 32 | 36 | 40 | |
| Below Average | 42 | 39 | 48 | |
| Total | 100 | 100 | 100 |
Advantages of Tabulation
Tabulation helps to achieve the following:
- It presents the data in easy to understand format.
- It reduces the voluminous size of data so as to view it in a comprehensive way
- It simplifies the data through grouping.
- It tries to highlight common features, salient points, characteristics, etc. from the data.
- Reveals underlying trends
- It allows easy comparison within the data or with other tabulated data.
- Data storage, reference, and retrieval at a later stage are very easy.
- Processing the data through spreadsheet packages like MS Excel can be done.
- Charting of graphs and diagrams is easy with tabulated data.
