FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs SUBJECT FORENSIC SCIENCE
Paper No. and Title PAPER No.15: Forensic Psychology
Module No. and Title MODULE No.26: Describing Data by Tables and Graphs
Module Tag FSC_P15_M26
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs TABLE OF CONTENTS
1. Learning Outcomes 2. Introduction
3. Tabulation of data
3.1 Difference between classification and tabulation 3.2 Significance of tabulation
3.3 Parts of a table
3.4 General rules of tabulation 3.5 Types of tables
4. Graphs
4.1 Rules for constructing a graph 4.2 Graphs of one variable
4.3 Graph of two or more variables 4.4 Band graph
4.5 Graphs of frequency distribution
Histogram
Frequency polygon
Smoothed frequency curve
Ogives or cumulative frequency curves 5. Pie Diagrams
6. Applications in Forensic Science 7. Summary
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 1. Learning Outcomes
After studying this module, you will be able to-
Know about the table and graphs
Various types of tables and graphs and their use
Forensic application of tables and graphs
2. Introduction
The very first step in analysis of data is to classify and tabulate the data. After classification the data is presented in the form of tables and graphs. The data can represented in a concise manner using graphs and tables but it is necessary to explain the data clearly. Classification and tabulation of data is not always interesting. Too many figures can be confusing sometimes and may fail to convey the message effectively. Another good and interesting way to represent a data is by using graphs and diagrams. There are various ways in which a data can be represented pictorially using graphs, diagrams, maps etc. Choosing the best way of representing the data is a difficult task and requires a great deal of artistic talent.
3. Tabulation of Data
One the easiest and best way to summarize data and present it in an efficient and meaningful way is statistical table. A table is a methodical preparation of statistical data in columns and rows. Rows are horizontal arrangements whereas columns are verticals ones. The basic objective of constructing a table is to simplify the presentation of the data and to ease comparisons. The simplification results from the precise and organized presentation of data which enables the reader to quickly locate desired information. Comparison is facilitated to bring related items of information close together.
3.1 Difference between Classification and Tabulation
Classification and tabulation are not two different processes. They go together in which classification is the first step in tabulation. Classification is necessary to put the data in tabular form. According to the various similar characteristics, the data is classified and tabulated. Only after classification the data is represented under rows and columns.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 3.2 Significance of Tabulation
Arrangement of large amount data in minimum space is achieved by using tables. Following points reflect the significance of tables:
It simplifies the complex data: Tabulation of data leads to exclusion of all repeated and unnecessary data. Systematic representation of data in rows and columns is achieved using tables which gives the reader a clear idea of what table presents. Since the heading and the data is not duplicated it saves space.
It facilitates comparison: Tabulation of data helps in comparison. The table is divided into several parts and for every part there are totals and subtotals. The relationship between various parts of the data can be easily studied with tables.
It gives identity to the data: When the data is tabulated, a title and number help to identify the source reference in the interpretation of the data.
It reveals patterns: The patterns within the figure which cannot be revealed through narrative data can be interpreted using tables.
3.3 Parts of a Table
The number of parts of a tables depends on types of data to be presented and variation from case to case. The basic parts used are:
Table number: numbering of each table should be done. The number can be given in center, at the top above or inside the title or at the top or bottom of the table.
Sometimes, if the number of columns is more, every column should be numbered.
Title of the table: suitable title to every table should be given. It is description of contents of table. It provides all the relevant answers about what precisely are the data in the table, location of the data and the time period of the data. It should be self- explanatory, brief and clear. Short titles can be read fast and easily as compared to long titles but it is sometimes necessary to put up long titles for the sake of clarity.
Font of the title should be prominent on the table.
Caption: It refers to column headings. It depicts whatever the column represent.
More than one column heading may or may not be present. It should be placed in the center of the column and should be precise and clear. The captions should be of smaller font size as compared with the main part of the table.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Stub: As distinguished from caption, these are designations of the rows and row headings. They are present towards the left and perform the same function for the horizontal rows of numbers in the table. They are usually wide as compared to column heading but should be kept as narrow as possible.
Body: The numerical information comprises of the body of the table. The most important part of the table. Data presented in the body arranged according to description are classification of the captions and stubs.
Headnote: It is a brief and precise explanatory statement applying to all or a major part of the material in the table and is placed below the point centered and enclosed in brackets. Headnotes are used for explanation of various facts which are not mentioned in the data or in captions or stubs.
Footnotes: Any fact or material which is not clear from the title, captions or stubs is explained in footnotes. They are placed directly below the table if required.
Format of a table
Title Headnote
Stub Heading Caption heading- Column heading
Stub Entries Body
Footnotes Table Number
3.4 General Rules of Tabulation
It is very difficult to lay down any strict rules for tabulating data because much depends upon the given data and requirements of the survey. Construction of a perfect and good table is an art and practical experience is of great help.
Following general considerations should be kept in mind while formation of tables:
It should be according to the size of the paper usually with more rows than columns.
Alteration of original design is sometimes necessary to make it in suitable layout.
Changing rows to columns or other way round are the basic alterations. Appropriate space for reference or any other data should be included in the table.
Arrangement of captions and stubs should be done is a systematic order. This systematic arrangement makes the table simplified and easier to read and understand.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Following ways of arranging the captions and stubs are usually followed:
o Alphabetical o Chronological o Geographical
o Conventional or in a customary order o According to size
The points of measurements should be clearly defined and given in the table.
Rounded figures should be used to avoid unnecessary details of table.
If emphasis have to be given to a particular figure, it should be in distinctive type or in box.
Overloading of tables should be avoided.
A column entitled miscellaneous should be added for data which doesn’t fit in the classification made.
Logical arrangement of table should be made and every item should be related to each other.
Computation of percentage and ratios should be done and shown.
Where standard classifications have been prepared it is usually desirable to employ them as they are superior to hastily constructed individual classification.
Avoid abbreviations, especially in headings and titles.
Be explicit
Ditto marks should be avoided.
3.5 Types of Tables
Tables can be broadly classified into two categories:
Simple and Complex tables
General purpose and special purpose tables
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 1. Simple and Complex tables:
According to the number of characteristics, distinction between simple and complex tables can be made. In a simple table, one characteristic is shown so it is known as one way table whereas complex table is known as two way table or double tabulation as two or more characteristics are shown. These tables are preferred as full information can be incorporated in them and facilitate proper consideration of all related facts. Those tables in which three characteristics are shown is known as treble tabulation.
For example:
One Way or Single Table: In this only one characteristic is shown.
NUMBER OF EMPLOYEES IN A COMPANY ACCORDING TO AGE GROUP
Age (in years) No. of employees
Below 25 years 8
25-30 20
35-45 15
45-55 5
Above 55 2
Total = 50
Two Way Table or Double Table: It shows two characteristics and is formed when either the stub or caption is divided into two coordinate parts.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
NUMBER OF EMPLOYEES OF A COMPANY IN DIFFERENT AGE GROUPS ACCORDING TO SEX
Age (in years) Employees No. of employees Males Females
Below 25 years 4 4 8
25-30 12 8 20
35-45 5 10 15
45-55 3 2 5
Above 55 1 1 2
Total = 50
2. General or Special purpose tables:
These are also known as reference tables or repository tables or derivative tables which provide information for general use or reference. They are not made for any special discussion, they contain detailed information. In other words, they are storehouse of information which are arranged for easy reference. They are also known as summary tables as they provide information for particular discussion. When they are attached to a report they are found in the body of the text. They are called derivative tables because they are often derived from general tables.
For example:
Age groups Literates Illiterates Total
M F M F M F Total
Below 25 years 4 4 1 5 5 9 14
25-30 12 8 2 2 14 10 24
35-45 5 10 5 8 10 18 28
45-55 3 2 8 10 11 12 23
Above 55 1 1 10 15 11 16 27
Total 25 25 26 40 51 65 116
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 4. Graphs
A large variety of graphs are used commonly. Graphs are classified under following categories:
Graphs of time series
Graphs of Frequency Distribution
Construction of charts and graphs is an art which can be acquired through practice. There are a number of rules, adoption of which leads to the effectiveness of graphs.
4.1 Rules for Constructing a Graph
Following points should be kept in mind while constructing a line graph:
Take the time on X axis and the variable on Y axis.
Begin Y axis with zero and select a suitable scale so that the entire data is accommodated in the space available.
Corresponding to the time factor plot the value of the variable and the various points by straight lines.
Join the various points with straight lines, not curves.
More than one graph should be distinguished by the use of dotted lines, thick or thin lines etc.
Appropriate title should be given to every graph.
Lettering on the graph should be done horizontally only.
4.2 Graphs of One Variable
In case of one variable, X axis represents time and y axis the value of variable. Various points are plotted accordingly and joined by straight lines. Variations in the variable is indicated by the fluctuation of this line.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 4.3 Graph of Two or More Variables
Two or more variables can be represented on the same graph in case of same units of measurement. This helps in comparison of data .But in case of large number of variables, this type of graph becomes quite confusing to understand. To distinguish between the variables and for sake of clarity of data broken, dotted or differently colored lines are used.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 4.4 Band Graph
It is a type of line graph which depicts the total for successive time periods broken up into subtotals for each of the component parts of the total. In short, it is a graph which shows how and in what proportion each item comprising the aggregate are distributed. Several component parts are plotted one over the other and the gaps between the successive lines are filled by different shades, colours etc.to give appearance of a series of bands.
4.5 Graphs of Frequency Distribution
These types of graphs can be presented in the following ways:
Histogram
Frequency polygon
Smoothed frequency curve
Ogives or cumulative frequency curves
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Histogram
It is one of the most popular and commonly used graphs .it is a set of vertical bars whose areas are proportional to the frequencies represented. X axis represents variables and frequencies depending on it are represented on Y axis .Each class is represented by a distance on the scale which is proportional to its class interval. If the class intervals are uniform the distance for each rectangle formed on X axis will be the same. They vary if they are different.
The Y axis represents the frequencies of each class which constitutes the height of its rectangle.
Bar diagrams and histograms should be clearly distinguished. The main difference between them is that a bar diagram is one dimensional in which only length of the bar is important whereas histogram is two dimensional in which both length and width are important.
Construction of a histogram is not possible with open end classes. If the distribution has unequal class intervals and suitable adjustments in frequencies are not made then a histogram can be quite misleading.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Frequency Polygon
It is a graph of frequency distribution and has more than four sides .It proves to be useful for comparison of two or more frequency distributions. Frequency polygon can be constructed in two ways:
We may draw a histogram of the given data and join by straight lines the mid points of the upper horizontal side of each rectangle with the adjacent ones. Such a figure is known as frequency polygon.
An alternate method construction of frequency polygon is to take the mid points of different class intervals and then plot the frequency corresponding to each point. Join these points by straight line, the figure so obtained will be same as the one obtained in previous method.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs Advantage of Frequency Polygon over Histogram
To make certain comparisons possible the frequency polygon of several distributions may be plotted on the same axis whereas in histogram a separate graph is required for each distribution.
It is comparatively simple.
The data pattern is clearly represented.
With the increase in number of classes and observations, the polygon becomes smoother and curve like.
Smoothed Frequency Curve
Various points of the polygon need to be considered while constructing a smoothed frequency curve. It is drawn freehand such that the included area under the curve is more or less the same as that of the polygon. Its main objective is to eliminate accidental variations that might be present in the data as far as possible.
The two steps for drawing a smoothed frequency curve are:
Draw the polygon
Smooth the polygon
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
While smoothing of curve, following points should be taken into consideration:
Only frequency distributions based on samples should be smoothed
Only continuous series should be smoothed.
The total area under the curve should be equal to the area under the original histogram or polygon.
Ogives or Cumulative Frequency Curves
Cumulative frequencies are the added frequencies which are listed in a table called cumulative frequency table. The curve obtained by plotting the cumulative frequencies is called cumulative frequency curve or an ogive.
Two ways of construction of ogives are:
o Less than method: In this we start with upper limits of classes and then keep on adding the frequencies to obtain a rising curve.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
o More than method: In this we start with lower limits and keep on subtracting the frequency of each class to obtain a declining curve.
Uses of Ogives
To find and show the number or proportion of cases above or below the given value.
For comparison of two or more frequency distributions.
For graphical determination of certain values such as medians, quartiles etc.
5. Pie Diagrams
Circlе diagrams arе altеrnativе to squarе diagrams and arе usеd for thе samе purposе which is for diagrammatic prеsеntation of thе valuеs diffеring widеly in thеir magnitudе. Thе arеa of thе circlе which rеprеsеnts thе givеn valuеs is givеn by 𝜋𝑟2, whеrе 𝜋 = 22/7 and r is thе radius of thе circlе. Just as subdividеd and pеrcеntagе bars or rеctanglеs arе usеd to rеprеsеnt thе total magnitudе and its various componеnts, thе circlе may bе dividеd into various sеctions or sеgmеnts which is sеctors rеprеsеnting cеrtain proportion or pеrcеntagе of thе various componеnt parts to thе total.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Such a sub-divided circlе diagram is known as angular or piе diagram/chart, namеd so bеcausе thе various sеgmеnts rеsеmblе slicеs cut from a piе.
Stеps of Construction of Piе Diagram
Еxprеss еach of thе componеnt valuеs as a pеrcеntagе of thе rеspеctivе total.
Sincе thе anglе at thе cеntеr of thе circlе is 360, thе total magnitudе of various componеnts is takеn to bе еqual to 360° and еach componеnt part is to bе еxprеssеd proportionatеly in dеgrееs.
Draw a circlе of appropriatе radius using an appropriatе scalе dеpеnding on thе spacе availablе. If only onе catеgory or charactеristic is to bе usеd, thе circlе may bе drawn of any radius.
Having drawn thе circlе, draw any radius. Now with this radius as thе basе linе draw an anglе at thе cеntеr еqual to thе dеgrее rеprеsеntеd by thе first componеnt. From this sеcond linе as basе, now draw anothеr anglе at thе cеntеr еqual to thе dеgrее rеprеsеntеd by thе 2nd componеnt, to givе thе sеctor rеprеsеnting thе proportion of thе sеcond componеnt. Procееding similarly, all thе sеctors rеprеsеnting diffеrеnt componеnt parts can bе constructеd.
Diffеrеnt sеctors rеprеsеnting various componеnt parts should bе distinguishеd from onе anothеr by using diffеrеnt shadеs, dottings, colours еtc. or giving thеm еxplanatory or dеscriptivе labеls еithеr insidе thе sеctor or just outsidе thе circlе with propеr idеntification.
Dеgrее of any componеnt part =𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒
𝑇𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
× 360°.
Еxamplе: Thе piе chart bеlow shows thе pеrcеntagеs of blood typеs for a group of 200 pеoplе.
a) How many pеoplе, in this group, havе blood typе AB?
b) How many pеoplе, in this group, do not havе blood typе O?
c) How many pеoplе, in this group, havе blood typеs A or B?
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Solution:
a) 19% × 200 = 19 × 200 / 100 = 38 people
b) (100% - 40%) × 200 = 60 × 200 / 100 = 120 people c) (16% + 25%) × 200 = 41 × 200 / 100 = 82
5. Application in Forensic Science
Tables and graphs are widely used in forensic science to tabulate the various evidences found and their findings. In case of stature estimation from bones, the measurements are tabulated for easy calculation and observation. Graphs are also plotted while determining time since death and to estimate the timings of wounds. In forensic psychology, techniques like polygraph involve plotting of graph to analyze and interpret the results.
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs
Tables and graphs are used in various branches of forensic science. Figure 1 shows tabulated data collected about victims in case of a mass disaster. This tabulated data helps in identification of victims.
Figure 1: Victim record after mass disaster
FORENSIC SCIENCE PAPER No.15: Forensic Psychology
MODULE No.26: Describing Data by Tables and Graphs 6. Summary
The very first step in analysis of data is to classify and tabulate the data
A table is a methodical preparation of statistical data in columns and rows
Arrangement of captions and stubs should be done is a systematic order.
According to the number of characteristics, distinction between simple and complex tables can be made.
In a simple table, one characteristic is shown so it is known as one way table whereas complex table is known as two way table or double tabulation as two or more characteristics are shown.
General or special purpose tables are storehouse of information which are arranged for easy reference.
A large variety of graphs are used commonly. Graphs are classified under following categories: Graphs of time series and Graphs of Frequency Distribution.
These types of graphs can be presented in the following ways: Histogram, Frequency polygon, Smoothed frequency curve and Ogives or cumulative frequency curves.
