Graphs(Biostatistics and Research Methodology) B.pharmacy(8th sem.)

GRAPHS
PREPARED BY:-
PRANJAL SAXENA
B.PHARMACY(8TH SEM.)
ORIENTAL UNIVERSITY
SUBMITTED TO:-
DR. NEELAM JAIN
ASSIOCIATE PROFESSOR
ORIENTAL UNIVERSITY

What is Statistics?
Statistics is the method of conducting a
study about a particular topic by
collecting, organizing, interpreting, and
finally presenting data.

GRAPHS AND IT’S TYPES
• Sometimes significance if figures (i.e. numbers) in tabular
presentation is not easily understood. In such cases, health
researchers and other executive prefer diagrammatic
presentation which is readily understood with the help of
graphs, charts or diagrams.
• Graphs of statistical data bring out clear and relative and are
helpful in finding out the relationship between two or more
sets of data.
• Types of Graphs
1. Line graph
2. Bar chart
3. Pie diagram
4. Histogram
5. Frequency
polygon

HISTOGRAM
• Histogram is a graphical representation of data where data is
grouped into continuous number ranges and each range corresponds
to a vertical bar.
• It is the most commonly used diagram to depict grouped frequency
distribution graphically.
• The horizontal axis displays the number range
• The vertical axis(frequency) represent the amount of data that is
present in each range.

Uncle Bruno owns a garden with 30 black cherry trees. Each tree is of a different
height. The height of the trees (in inches): 61, 63, 64, 66, 68, 69, 71, 71.5, 72, 72.5, 73,
73.5, 74, 74.5, 76, 76.2, 76.5, 77, 77.5, 78, 78.5, 79, 79.2, 80, 81, 82, 83, 84, 85, 87.
Height
(Ft)
60-65 66-70 71-75 76-80 81-85 86-90
No. of
Trees(fre
quency)
3 3 8 10 5 1
EXAMPLE:-
61, 63, 64, 66, 68, 69, 71, 71.5, 72, 72.5, 73, 73.5, 74, 74.5,
76, 76.2, 76.5, 77, 77.5, 78, 78.5, 79, 79.2, 80, 81, 82, 83,
84, 85, 87

The histogram for a frequency distribution given
below:-
Answer the following.
(1.) What is the frequency of the class
interval 15 – 20?
(2.) What is the class intervals having the
greatest frequency?
(3.) What is the cumulative frequency of the
class interval 25 – 30?
Answer:-
1. 25
2. 20-25
3. 90

ADVANTAGES AND DISADVANTAGES
DISADVANTAGES
• Use only with continuous data
• More difficult to compare two data sets
• Cannot read exact values because data
is grouped into categories.
ADVANTAGES
• Works well when the data has a REALLY
BIG range
• There is one set of data
• Data collected using a frequency table
• Provides a way to display the frequency of
occurrence of data along with interval.
• It assist in decision making
• It summarize large data

PIE-CHART
• A pie chart is a type of graph that
represents the data in the circular
graph. The slices of pie show the
relative size of the data. It is a type
of pictorial representation of data. A
pie chart requires a list of categorical
variables and the numerical variables.
Here, the term “pie” represents the
whole, and the “slices” represent the
parts of the whole.
• The “pie chart” is also known as
“circle chart”, that divides the circular
statistical graphic into sectors or slices
in order to illustrate the numerical
problems. Each sector denotes a
proportionate part of the whole. To
find out the composition of
something, Pie-chart works the best at
that time.

EXAMPLE
61%
27%
8%4%
PIE-CHART
Tuberculoid
Lepromatous
Indeterminate
Borderline
TYPES OF
LEPROSY
No. of
patients
Percentages Degrees
Tuberculoid 148 61.7 32.2
Lepromatous 64 26.7 96
Indeterminat
e
18 7.5 27
Borderline 10 4.1 15
TOTAL 240 100.0 360

ADVANTAGES AND DISADVANTAGES
OF PIE-CHART
• ADVANTAGES
1. Give audience the best visual for
statistics
2. You can under stand with little
knowledge of math
3. It can summarize a large set of data
with minimal explanation
4. Easier to understand than other
graphs and easier to set up.
• DISADVANTAGES
1. A pie chart have only one set of data
2. It is hard to tell which section are
bigger
3. You can only use it for expressing
data out of a whole
4. There is no numerical data.

CUBIC GRAPH
• A cubic graph is a graph in which
all vertices have degree three(3D).
In other words, a cubic graph is a
3-regular graph.
• Cubic graphs are also called trivalent
graphs
• If the smallest and the largest
magnitude to be presented as in the
ratio of 1:1000, the bar diagrams
cannot be used because of the
height of the biggest bar would be
1000 times the height of the
smallest bar and thus they would
look very disproportionate.

• The various step are below:-
1. Construct a square of side ABCD.
2. Draw EF as bisector perpendicular to bisector of AB[this is done by finding
the mid point of AB and then drawing a perpendicular at the point line to
AB] such that EF =AB
3. Join AE,CF, and EF.
4. Through B draw a line BG parallel to AE, such that BG-AE.
5. Join EG and through G draw a line GH║EF such that GH=EF
6. Join DH
7. Rub off the lines CF, EF and FH. Now CDHGEAC is the required cube
• If we take squares of the sides if the square 1:√1000 i.e. 1:31.62 i.e.1:32(approx.) which
will again disproportionate diagrams.
• If cube are used to the present this data, then the volume of cube of side is ‘x’ then we
take the cube roots i.e.1:
• i.e. 1:10, which will give to a reasonably proportionate diagram
Construction of a cube of side ‘AB’

EXAMPLE
The following data gives the population of India on the basis of
religion
RELIGION Hinduism Islam Christianity Sikhism Others
No.(in lakhs) 2031.9 354.0 81.6 62.2 36.1
Sol. The sides of the cubes will be proportional to the cube roots of the
magnitudes they represent
To calculate cube root of ‘a’
3√a or a1/3
Let y= 3√a= a1/3
Taking logarithm both sides
Log y = 1/3 log10a
Log y = 1/3 log10a
y= AntiLog[1/3 log10a]

a log10a 1/3 log10a AntiLog[1/3
log10a]
Ratio of sides
2031.9 3.3079 1.1026 12.67 3.83(3.8)
354.0 2.5441 0.8480 7.047 2.13(2.1)
81.6 1.9117 0.6372 4.337 1.31(1.3)
62.2 1.7938 0.5979 3.962 1.19(1.2)
36.3 1.5599 0.5199 3.311 1
Hinduism(3.8) Islam(2.1) Christianity(1.3) Sikhism(1.2) others(1)

RESPONSE SURFACE PLOT
Surface plots are diagrams of three-
dimensional data. Rather than showing
the individual data points, surface
plots show a functional relationship
between a designated dependent variable
(Y), and two independent variables (X
and Z). The plot is a companion plot to
the contour plot.
A 2-D grid of X and z is constructed.
The range is grid is equal to the range of
the data. A ‘Y’ value is calculated for each
grid point. This Y value is a weighted
average of all data that is near this grid
point.
The 3-D surface is constructed using
these averages values. Hence, the surface
plot does not show the variation at each
grid point.

• Remember that multiple regression
assumes that this surface is a
perfectly flat surface.
• The 3-D surface is constructed
using these averaged values. Hence,
the surface plot does not show the
variation at each grid point.
• These plots are useful in regression
analysis for viewing the relationship
among a dependent and two
independent variables.
RESPONSE SURFACE PLOT

CONTOUR PLOT GRAPH
• Many others disciplines use contour
graph including astrology, meteorology
and physics.
• Contour lines commonly shows
altitude height of geographical area.
• Also be used to show density,
brightness, or electric potential.
• Contour plots (sometimes called Level
Plots) are a way to show a 3-D surface
on a 2-D plane. It graph two predictor
variables XY on the axis and a
response variable Z as contours.
• This type of graph is widely used in
cartography, where contour lines of
topological map indicate elevation that
are the same.

TYPES OF CONTOUR PLOT
1. RECTANGUALR CONTOUR
PLOT
2. POLAR CONTOUR PLOTS

TYPES
• Ternary plots are triangular and
show a relationship between three
explanatory variables and a
response variable. Most commonly,
the third explanatory variable is a
height value for an XYZ value in
ternary space.

Graphs(Biostatistics and Research Methodology) B.pharmacy(8th sem.)

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