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Tabulation

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Objectives of Data Tabulation

� To carry out investigations

� To do comparisons

� To locate omissions and errors in the data

� To use space economically

� To study the trends

� To simplify data

� To use it as future references

Sessio

n 01

Importance of Tabulation

� Under tabulation, data is divided into various parts and for each part there are totals and sub totals. Therefore, relationship between different parts can be easily known.

� Since data are arranged in a table with a title and a number so these can be easily identified and used for the required purpose

� Tabulation makes the data brief. Therefore, it can be easily presented in the form of graphs.

� Tabulation presents the numerical figures in an attractive form.

Sessio

n 01


� Tabulation makes complex data simple and as a result of this, it becomes easy to understand the data.

� This form of the presentation of data is helpful in finding mistakes.

� Tabulation is useful in condensing the collected data.

Sessio

n 01


� Tabulation makes it easy to analyze the data from tables.

� Tabulation is a very cheap mode to present the data. It saves time as well as space.

� Tabulation is a device to summaries the large scattered data. So, the maximum information may be collected from these tables.

Sessio

n 01

Rules of Tabulation

� The table should suit the size of the paper and, therefore, the width of the column should be decided before hand.

� Number of columns and rows should neither be too large nor too small.

� As far as possible figures should be approximated before tabulation. This would reduce unnecessary details.

There are no hard and fast rules for the tabulation ofdata but for constructing good table, following generalrules should be observed while tabulating statisticaldata.

Sessio

n 01

Rules of Tabulation

� Items should be arranged either in alphabetical, chronological or geographical order or according to size.

� The sub-total and total of the items of the table must be written.

� Percentages are given in the tables if necessary.

� Ditto marks should not be used in a table because sometimes it create confusion.

� Table should be simple and attractive.

Sessio

n 01

Rules of Tabulation

� A table should be logical, well-balanced in length and breadth and the comparable columns should be placed side by side.

� Light/heavy/thick or double rulings may be used to distinguish sub columns, main columns and totals.

� For large data more than one table may be used.

Sessio

n 01

Parts of an Ideal Table

� Table number:

A number must be allotted to the table for identification, particularly when there are many tables in a study.

� Title:

The title should explain what is contained in the table. It should be clear, brief and set in bold type on top of the table. It should also indicate the time and place to which the data refer.

Sessio

n 01

Parts of an Ideal Table � Date:

The date of preparation of the table should be given.

� Stubs or Row designations:

Each row of the table should be given a brief heading. Suchdesignations of rows are called “stubs”, or, “stub items” andthe entire column is called“stub column”.

� Column headings or Captions:

Column designation is given on top of each column toexplain to what the figures in the column refer. It should beclear and precise. This is called a “caption”, or, “heading”.columns should be numbered if there are four, or, morecolumns.

Sessio

n 01

Parts of an Ideal Table� Body of the table:

The data should be arranged in such a way that any figure can be located easily. Various types of numerical variables should be arranged in an ascending order, i.e., from left to right in rows and from top to bottom in columns. Column and row totals should be given.

� Unit of measurement: If the unit of measurement is uniform throughout the table, it is stated at the top right-hand corner of the table along with the title. If different rows and columns contain figures in different units, the units may be stated along with “stubs”, or, “captions”. Very large figures may be rounded up but the method of rounding should be explained.

Sessio

n 01

Parts of an Ideal Table

� Source:

At the bottom of the table a note should be added indicating the primary and secondary sources from which data have been collected.

� Footnotes and references:

If any item has not been explained properly, a separate explanatory note should be added at the bottom of the table.

Sessio

n 01

Limitation of Tabulation

� Tables contain only numerical data. They do not contain details.

� qualitative expression is not possible through tables.

� Tables can be used by experts only to draw conclusions. Common men do not understand them properly.

Sessio

n 01

Methods of Tabulation

� Simple tabulation

Simple tabulation is when the data aretabulated to one characteristic. Forexample, the survey that determined thefrequency or number of employees of afirm owning different brands of mobilephones like Blackberry,Nokia, Iphone, etc.

Sessio

n 02


�Double tabulation

Double tabulation is when two characteristics of data

are tabulated. For example, frequency or number ofmale and female employees in the firm owning differentbrand of mobile phones like Blackberry, Nokia, Iphone,etc.

Sessio

n 02


� Complex tabulation

Complex tabulation of data that includes more than

two characteristics. For example, frequency or numberof male, female and the total employees owningdifferent brand of mobile phones like Blackberry, Nokia,Iphone, etc. Crosstabulations, is also a sub-type ofcomplex tabulation that includes cross-classifyingfactors to build a contingency table of counts orfrequencies at each combination of factor levels. Acontingency table is a display format used to analyze andrecord the possible relationship between two or morecategorical variables

Sessio

n 02

Frequency Tables

� Simple frequency tables

� Grouped frequency tables

� Cumulative frequency tables

Sessio

n 03

Simple Frequency Tables

� If the value of a variable, e.g., height, weight, etc. (continuous), number of students in a class,

� readings of a taxi-meter (discrete) etc., occurs twice or more in a given series of observations,

then

the number of occurrence of the value is termed as the “frequency” of that value.

Sessio

n 03


Marks of 100 students of a class in economics

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n 03


Simple frequency table for marks

Sessio

n 03

Grouped Frequency Tables

The tabulation of raw data by dividing the whole rangeof observations into a number of classes and indicatingthe corresponding class-frequencies against the class-intervals, is called “grouped frequencydistribution”.

Thus the steps in preparing the grouped frequency distribution are:

1. Determining the class intervals.

2. Recording the data using tally marks.

3. Finding frequency of each class by counting the tally arks.

Sessio

n 04


� Class-limits: The maximum and minimum values of a class-interval are called upper class limit and lower class-limit respectively

� Class-mark, or, Mid-value: The class-mark, or, mid-value of the class-interval lies exactly at the middle of the class-interval

Important Terms

Sessio

n 04


� Class boundaries: Class boundaries are the true-limitsof a class interval. It is associated with groupedfrequency distribution, where there is a gap betweenthe upper class-limit and the lower class-limit of thenext class.This can be determined by using the formula:

where d = common difference between the upper class-limit of a class-interval and the lower class limitof the next higher class interval

Sessio

n 04


� Width or Length (or size) of a Class-interval: Width of a class-interval = Upper class boundary −Lower class-boundary

� Relative frequency:

Sessio

n 04


� Percentage frequency:

� Frequency density:

Sessio

n 04

Grouped Frequency TablesTypes of Grouped tables

Exclusive type

X f

10 – 15 XX

15 – 20 XX

20 – 25 XX

25 – 30 XX

Upper limit excluded

Sessio

n 04


Exclusive type

X f

Above 10 but no more than 15 XX




Lower limit excluded

Sessio

n 04


Exclusive types

Upper limit excluded

X f

30 - XX

40 - XX

50 - XX

60 -70 XX

Sessio

n 04


Inclusive type

X f

30 – 39 XX

40 – 49 XX

50 – 59 XX

60 – 69 XX

Sessio

n 04


Open – End Type

X f

0 – 10 XX

10 – 20 XX

20 – 30 XX

30 – over XX

X f

Below 30 XX

30 – 40 XX

40 – 50 XX

50 and over XX

Sessio

n 04


Unequal class intervals

X f

10 – 30 XX

30 – 35 XX

35 – 40 XX

40 – 60 XX

60 – 70 XX

70 – 100 XX

Sessio

n 04

Multivariate Frequency TablesThe multivariate frequency table is a statistic method to

organize and simplify a large set of data of two or morevariables in a single table.

Example:

Sessio

n 05

Multivariate Frequency Tables

Example: Multivariate frequency table

Sessio

n 05


Example: Marginal frequency tables for X and Y

Sessio

n 05


Example: Conditional Distribution X when Y Lies Between 300 and 400

Sessio

n 05

Cumulative Frequency Tables

The cumulative frequency table of a set of data is a tablewhich indicates the sum of the frequencies of the dataup to a required level. It can be used to determine thenumber of items that have values below a particularlevel.

Example: Construct the cumulative frequency distribution (both“less than” and “more than” types) from the following data:S

essio

n 06

Cumulative Frequency Tables

Example: Cumulative frequency table

Sessio

n 06

Cross TabulationCross-tabs or cross tabulation is a quantitative research

method appropriate for analyzing the relationship betweentwo or more variables. Data about variables is recorded ina table or matrix. A sample is used to gather informationabout the variable.

Cross Tabulation gives you the ability to compare twoquestions to each other and evaluate relationships betweenthe responses of those questions. You can review thefrequency and assess the statistical significance in thatrelationship. Cross tabulation is particularly useful when youwant to assess whether there is a relationship between howyour entire respondent base, or a specific subset ofrespondents, answered two questions.

Sessio

n 07 &

8

Cross Tabulation

General Hints When Constructing Tables

1. Make sure that all the categories of the variables presented in the tables have been specified and that they are mutually exclusive (i.e.

no overlaps and no gaps) and exhaustive.

2. When making cross-tabulations, check that the column and row

counts correspond to the frequency counts for each variable.

3. Check that the grand total in the table corresponds to the number of subjects in the sample. If not, an explanation is required. This could

be presented as a footnote. (Missing data, for example.)

4. Think of a clear title for each table. Also be sure that the headings of

rows and columns leave no room for misinterpretation.

5. Number your tables and keep them together with the objectives to

which they are related. This will assist in organizing your report and ensure that work is not duplicated.

Sessio

n 07 &

8

Cross Tabulation - Descriptive Cross Tabulation

Example 1:A study was carried out on the degree of job satisfaction among doctors

and nurses in rural and urban areas. To describe the sample a cross-tabulation was constructed which included the sex and the residence

(rural or urban) of the doctors and nurses interviewed. This was useful

because in the analysis the opinions of male and female staff had to becompared separately for rural and urban areas.

Type of health worker by residence

Sessio

n 07 &

8

Cross Tabulation - Descriptive Cross Tabulation

Residence and sex of doctors and nurses

Sessio

n 07 &

8

Example 2:We want to know the ages at which teenage pregnancies occur and

whether they are more frequent among schoolgirls than among girls whoare not attending school. In order to answer these questions we may

construct the following cross-tabulation.

Number of teenage pregnancies at different ages among girls attending school and not attending school (Province X, 2000 - 2010)

Cross Tabulation - Descriptive Cross TabulationS

essio

n 07 &

8

Example 3:A study was done to examine the factors contributing to the high

proportion of stillbirths in a hospital. The following cross-tabulationdescribes how many of the fresh and macerated (wasted) stillbirths

weighed less than 2500 grams and how many weighed 2500 grams or

more.

Weight of foetus by condition at birth


essio

n 07 &

8

Example 4:In a cross-sectional survey on malnutrition, for example, relationships

could be tested between the duration of breastfeeding and the mothers’ age, or the mothers’ working status (answering previously formulated

research questions, but sometimes new questions that crop up during

analysis of the material).

Note that in such tables it is allowed to calculate your percentages both horizontally and vertically as all variables have a similar chance of appearing in the survey. However, we will usually put the variable that is

assumed to influence the other one in rows, while the ‘dependent’ variable will be put in columns


essio

n 07 &

8

Duration of breastfeeding by mothers’ age

Working status of mothers in relation to duration of breastfeeding


essio

n 07 &

8

Cross Tabulation - Analytic cross-tabulations

Example 5:One of the possible contributing factors to malnutrition of under 5’s is

knowledge of the mothers of appropriate weaning foods. The cross-sectional comparative study on malnutrition based on the survey gave

the following results

Mothers’ level of knowledge and nutritional status of their children

Sessio

n 07 &

8

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