Tabulation of data

1. Tabulation

2. 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

3. Rules of Tabulation:
There are no hard and fast rules for the tabulation of data
but for constructing good table, following general rules
should be observed while tabulating statistical data.
⚫ 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.
⚫ Items should be arranged either in alphabetical,
chronological or geographical order or according to size.

4. ⚫ 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.
⚫ 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.

5. Parts of an
Ideal Table
Table number
Title
Date
Stubs
or
Row designations
Column headings
Or
Captions
Body of the table
Source
Footnotes
&
references

6. ⚫ Table number:
Anumber 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.
Parts of an Ideal Table

7. ⚫ 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. Such
designations of rows are called “stubs”, or, “stub items” and
the entire column is called “stub column”.
⚫ Column headings or Captions:
Column designation is given on top of each column to explain
to what the figures in the column refer. It should be clear and
precise. This is called a “caption”, or, “heading”. columns
should be numbered if there are four, or, more columns.

8. ⚫ 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.
⚫ 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.

9. 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.

10. ⚫ 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.
⚫ 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.

11. 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.

12. Methods of Tabulation
⚫ Simple tabulation
Simple tabulation is when the data are tabulated to one
characteristic. For example, the survey that determined
the frequency or number of employees of a firm owning
different brands of mobile phones like Blackberry,
Nokia, I phone, etc.
⚫ Double tabulation
Double tabulation is when two characteristics of data are
tabulated. For example, frequency or number of male
and female employees in the firm owning different
brand of mobile phones like Blackberry, Nokia, Iphone,
etc.

13. ⚫ Complex tabulation
Complex tabulation of data that includes more than two
characteristics. For example, frequency or number of
male, female and the total employees owning different
brand of mobile phones like Blackberry, Nokia, I phone,
etc. Cross tabulations, is also a sub-type of complex
tabulation that includes cross-classifying factors to build
a contingency table of counts or frequencies at each
combination of factor levels. A contingency table is a
display format used to analyze and record the possible
relationship between two or more categorical variables

14. Frequency Tables
1. Simple frequency tables
2. Grouped frequency tables
3. Cumulative frequency tables

15. 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.

16. Simple Frequency Tables
Marks of 100 students of a class in economics

17. Simple frequency table for marks

18. Grouped Frequency Tables
The tabulation of raw data by dividing the whole range
of observations into a number of classes and indicating
the corresponding class-frequencies against the class-
intervals, is called “grouped frequency distribution”.
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
marks.

19. Important Terms in Grouped
Frequency Tables
⚫ 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
Session
04

20. ⚫ Class boundaries: Class boundaries are the true-limits
of a class interval. It is associated with grouped
frequency distribution, where there is a gap between the
upper class-limit and the lower class-limit of the next
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
limit
of the next higher class interval

21. ⚫ Width or Length (or size) of a Class-interval: Width
of a class-interval = Upper class boundary − Lower
class-boundary
⚫ Relative frequency:
⚫ Percentage frequency:
Session
04

22. ⚫ Frequency density:

23. 1. Upper limit Included
2. Lower limit Excluded
3. Upper limit Excluded
4. Inclusive Type
5. Open-End Type
6. Unequal Intervals
Types of Grouped Frequency Tables:

24. X f
10 – 15 XX
15 – 20 XX
20 – 25 XX
25 – 30 XX
1.Upper limit Excluded

25. X f
Above 10 but no more than 15 XX
Above 15 but no more than 20 XX
Above 20 but no more than 25 XX
Above 25 but no more than 35 XX
2. Lower limit Excluded

26. 3.Upper limit Excluded
X f
30 - XX
40 - XX
50 - XX
60 - 70 XX

27. 4. Inclusive type
X f
30 – 39 XX
40 – 49 XX
50 – 59 XX
60 – 69 XX

28. 5. 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

29. 6.Unequal class intervals
X f
10 – 30 XX
30 – 35 XX
35 – 40 XX
40 – 60 XX
60 – 70 XX
70 – 100 XX

30. Cumulative Frequency Tables
The cumulative frequency table of a set of data is a table
which indicates the sum of the frequencies of the data up
to a required level. It can be used to determine the
number of items that have values below a particular
level.

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

32. Cross Tabulation
Cross-tabs or cross tabulation is a quantitative research
method appropriate for analyzing the relationship between
two or more variables. Data about variables is recorded in
a table or matrix. A sample is used to gather information
about the variable.
Cross Tabulation gives you the ability to compare two
questions to each other and evaluate relationships between
the responses of those questions. You can review the
frequency and assess the statistical significance in that
relationship. Cross tabulation is particularly useful when
you want to assess whether there is a relationship between
how your entire respondent base, or a specific subset of
respondents, answered two questions.

33. General Hints When Constructing Tables Cross
Tabulation :
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.

34. Cross Tabulation - Descriptive Cross Tabulation
Example :
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 be compared separately for rural and
urban areas.
Type of health worker by residence

35. Cross Tabulation - Analytic cross-tabulations
Example :
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