This document discusses various methods for diagrammatic and graphical representation of statistical data. It describes one-dimensional, two-dimensional, and three-dimensional diagrams as well as pictograms and cartograms. Specific diagram types discussed include line diagrams, bar diagrams, pie charts, and histograms. Graphical representations like line graphs, frequency polygons, frequency curves, and cumulative frequency curves are also covered. The key differences between bar diagrams and histograms are highlighted.

1. Diagrammatic and Graphical
Representation of Data
• One of the most convincing and appealing ways in
which statistical results may be presented is
through diagrams and graphs
• Usefulness of diagrams & graphs:
– give a bird’s eye view of the entire data and therefore
the information presented is easily understood.
– are attractive to the eye. Figures are dry but diagrams
delight the eye.
– have a great memorizing effect.
– facilitate comparison of data relating to different
periods of time or different regions

2. Types of diagrams
• One dimensional diagrams eg. Line
diagram, Bar diagram
• Two dimensional diagrams eg. Rectangles,
squares & circles.
• Three dimensional diagrams eg. Cubes,
cylinders & spheres.
• Pictograms & Cartograms.

3. Line diagram
• is used in case where there
are many items to be
shown and there is not
much of difference in their
values
• by drawing a vertical line
for each item according to
the scale

4. Bar diagram
• Most commonly used. A bar
is a thick line whose length
is considered and hence,
called one dimensional.
• There are four types of bar
diagrams.
– Simple bar diagram.
– Sub divided bar diagram or
component bar diagram.
– Multiple bar diagram
– Percentage bar diagram

5. Simple bar

6. Multiple bar

7. Sub-divided bar

8. Percentage bar

9. 2-dimensional bar

10. 2-dimensional bar

11. Pie – diagram
• A circular diagram and used to
present the different components of
a qualitative character
• The different components are
represented by means of sectors of
a circle.
• The angles of the sectors are
calculated as the fractions of 360
degree
• angles of the sectors are
proportional to the given quantities.

12. 3-dimensional bar

13. Pictogram

14. Graphical representation
Graphs are of two types:
1) Graphs of time series or Line graphs
2) Graphs of frequency distributions:
• Histogram
• Frequency polygon
• Frequency curve
• ‘Ogives’ or cumulative frequency curves
• Lorenz curve

15. Histogram
• is a set of vertical bars whose areas are
proportional to the frequencies represented
• histogram the variable is taken on the X-axis
and the frequencies on the Y-axis
• we get a series of rectangles each having a
class-interval distance as its width and the
frequency distance as its height
• Thus, it is two dimensional
• widely used to represent frequency distribution
• can not be constructed for distribution with
open-end classes

16. Difference b/n Bar diagram &
Histogram

17. Frequency polygon
• can be obtained by joining the mid-points
of the upper horizontal side of each
rectangle with the adjacent ones of the
histogram by means of straight lines
• may also be drawn independently without
drawing a histogram.
• For this mid-point values are marked on a
suitable scale along the ‘X’ axis and then
points are plotted vertically above them at
heights proportionate to the frequencies of
those class intervals and then by serially
joining these points by straight lines

18. Frequency curve
• the mid points of the upper
edges of the rectangle are
joined by a free hand
smooth curve
• may not pass through all
points as in the case of a
frequency polygon
• is a continuous curve
showing the nature of
distribution of
observations.

19. Cumulative frequency curves
• The free hand lines obtained by
plotting cumulative frequencies,
against the mid points of the class
intervals
• two methods of constructing
– ‘less than’ method upper limits are
taken on the X-axis and the
cumulative frequencies on the Y-
axis
– ‘more than’ method lower limits of
the classes are taken on the X-axis
and the cumulative frequencies on
the Y-axis

20. Lorenz curve
• graphical method of
studying dispersion
• graphical representation of
income inequality or
wealth inequality.
• The modification of the
Ogive when the variables
and the cumulative
frequencies are expressed
as percentages