It will give idea about Graphical and Diagrammatic Representation of Data

1. Lecture 3. Graphical and
diagrammatic representation of data
Dr. Ashish. C. Patel
Assistant Professor,
Dept. of Animal Genetics & Breeding,
Veterinary College, Anand
STAT-531
Data Analysis using Statistical Packages

2. • Main aim of statistics is to reduce the huge mass
of data to draw some definite conclusions about
the population.
• For that classification and tabulation of data can
be use.
• But tables also generally do not make the whole
thing clear at a single glance.
• If they are presented by some kind of diagram, the
relation between the quantities can be very easily
illustrated, since a pictorial representation usually
makes a clearer impression on the mind than the
numerical.
• Statistical data visualize in the form of points,
lines, areas, symbols and other geometrical forms
is known as Graphical Representation.

3. • The basic difference between a graph and a
diagram is that a graph is a representation of
data by a continuous curve, usually shown on a
graph paper while a diagram is one, two or
three-dimensional form of visual representation
on plain paper.
• The advantages of diagrammatic representations
are
• 1) It provides attractiveness and effectiveness to
the observed data
• 2) It is easily understood by experts and non-
experts
• 3) It saves the valuable time.

4. • Simple Bar Diagrams are made to represent
geographical, historical, numerical and the qualitative
data. The vertical or horizontal bars are made to
represent the data.
204.6
198.9
185.2
199.1
190.9
1 99 2 1 9 97 2 00 3 2 00 7 2 0 12
CATTLE POPULATION OF INDIA (IN MILLION
NUMBER)
204.6
198.9
185.2
199.1
190.9
84.2
89.9
97.9
105.3
108.7
1 99 2 19 9 7 2 00 3 2 00 7 20 1 2
CATTLE AND BUFFALO POPULATION OF INDIA (IN
MILLION NUMBER)
Cattle Buffalo
Simple Bar Diagrams Multiple Bar diagrams
A multiple bar diagram in which two or more
characteristics with their values in form of bars.
One dimensional diagrams

5. • A sub-divided bar diagram in which each bar is divided into two or
more sections, proportional in size to the component parts
Pie chart or pie diagram in which circle is divided into pie shaped
pieces, whose areas are proportional to quantity. Draw a circle
which consists 360° angle.
Find out the corresponding proportions in form of angles by
formula. Angle = (Component / Total Quantity) x 360°. Draw the
circle of corresponding angles.
0
50
100
150
200
250
300
350
1992 1997 2003 2007 2012
CATTLE AND BUFFALO POPULATION OF INDIA (IN MILLION
NUMBER)
Cattle Buffalo
Sub-divided Bar diagrams Pie diagram

6. Other types of diagrams are Line Diagram, Percentage sub-divided
bars, Deviation Bar and Broken Bar.

7. • In two dimensional diagrams, the areas instead of
lengths are proportional to the given figures. The
important diagrams of these types are
• a). Rectangle: use when two quantities are proportional
to third quantity. One quantity represents by length of
rectangle, second quantity represents by width of
rectangle and third quantity represent by area of
rectangle.
• b). Squares: data can also be represented in 3D
diagrammatic form such as Rectangular solids and cubes.
• Three dimensional diagrams: In this type of diagram we
can use cubes, spheres, prisms, cylinders etc.
• Pictograms: In this type of diagram we can use pictures
to represents the data.
Two dimensional diagrams

9. • Graphical Representation of Data
• Graphical representation is used when we have
to represent frequency distribution data and
time series data.
• Graphs of frequency distribution reveal clearly
the characteristic feature of a frequency data.
• The most commonly used graphs are:
a). Histogram
b). Frequency polygon
c). Frequency curve
d). “Ogive” curve or Cumulative Frequency Curve

10. • The choice of a particular graph depends on the
nature of the frequency distribution viz. discrete or
continuous
• a). Histogram: It is one of the most popular and
commonly used devices for charting continuous
frequency distribution.
• It consists a series of adjacent vertical rectangles on
the X-axis, with bases (Sections) equal to the width
of the corresponding class intervals and heights are
so taken that areas of the rectangles are equal to
the frequencies of the corresponding classes.
• The width of the rectangles is in proportion to the
class intervals under consideration, and their areas
represent the relative frequency.

11. • Histogram with equal classes: In the case, if classes are
of equal magnitude throughout, each class interval is
drawn on X-axis by base (of the rectangle) which is
equal (or proportional) to the magnitude of the class
interval.
• The height proportional to the corresponding frequency
of the class.

12. • Histogram with unequal classes: If all classes are not
uniform, the different classes are represented on the
X-axis by sections or bases which are equal (or
proportional) to the magnitudes of the corresponding
classes and the heights of the corresponding
rectangles are to be adjusted so that the area of the
rectangle is equal to the frequency of the
corresponding class.
• This adjustment can be done by taking the heights of
each rectangle proportional to the corresponding
frequency density of each class which is obtained on
dividing the frequency of the class by its magnitude.

13. Weekly Wages
(’00 Rs.)
No. of workers
(f)
Magnitude of class Height of rectangle
20-25 27 5 27
25-30 15 5 15
30-40 12 10 (12/2)=6
40-60 12 20 (12/4)=3
60-80 8 20 (8/4)=2

14. Frequency Polygon
• Frequency Polygon is graphical representation of a
frequency distribution (continuous, grouped or
discrete).
• 1. Frequency Polygon from histogram: First draw the
histogram of the given frequency distribution.
• Now joins the mid-points of the tops (upper horizontal
sides) of the adjacent rectangles of the histogram by
straight line graph. The figure obtained is called a
Frequency polygon (Polygon is figure with more than
four sides).

15. • Frequency Polygon without Histogram: Frequency
Polygon of a grouped or continuous frequency
distribution is a straight line which can also be
constructed directly without drawing histogram.
• This consists in plotting the frequencies of
different classes (along Y-axis) against the mid
vales of the corresponding classes (along X-axis).
The points so obtained are joined by straight lines
to obtain the frequency polygon.

16. • Histogram is a two dimensional figure, viz., a
collection of adjacent rectangles whereas
frequency polygon is a line graph.
• Frequency polygon can be used more
effectively for comparative study of two or
more frequency distributions because
polygons of different distribution can be
drawn on single graph.

17. Frequency Curve
• A frequency curve is a smooth free hand curve drawn
through the vertices of a frequency polygon.
• The purpose of smoothing of the frequency polygon is
to eliminate, as far as possible, the random or erratic
fluctuations that might be present in the data.
• A frequency curve can provide where, the frequencies
rises gradually to the highest point and then falls more
or less in the same manner. It also enables us to have an
idea about the Skewness.

18. Types of frequency curves:
• 1. Curves of Symmetrical distribution: In a symmetrical
distribution, the class frequency first rise steadily, reach
maximum and then diminish in the same identical manner.
• If a curve is folded symmetrically about a vertical line
(corresponding to the maximum frequency), so that the two
halves of the figures coincide, is called a Symmetrical curve.
• It has a single smooth hump in the middle and tappers off
gradually at either end and is bell-shaped.

19. • 2. Moderately Asymmetrical (Skewed) frequency
curves: A frequency curve is said to be skewed
(asymmetrical) if it is not symmetrical.
• Such curves are stretched more to one side than to
the other side.
• If the curve is stretched more to right (i.e. has a longer
tail towards the right), it is said to be positively
skewed and if it is said stretched more to the left (i.e.
has a longer tail towards left), it is said to be
negatively skewed.

21. Ogive (Cumulative Frequency Curve)
• Ogive, pronounced as ojive, is a graphic presentation of
the cumulative frequency (c.f.) distribution of
continuous variable.
• Since there are two types of cumulative frequency
distribution viz. ‘less than cumulative frequencies’ and
‘more than cumulative frequencies’ so, accordingly two
types of ogives, ‘less than’ ogive and ‘more than’ ogive.

22. Marks No. of Students Less than C.F. More than C.F.
0-10 10 10 60
10-20 15 25 50
20-30 20 45 35
30-40 8 53 15
40-50 7 60 7