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Stochastic Methods
Topic: Introductory Statistics
Dr. Nasir M Mirza
Computational Physics
Computational Physics
Email: [email protected]
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Lecture Notes: Monte Carlo Methods, Variables, Graphs, and Data Plotting, Slides of Computational Physics
A collection of lecture notes on introductory statistics, specifically focusing on monte carlo methods, types of variables, graphs, and data plotting. The notes cover the basics of statistics, including the concepts of population and sample, inductive and deductive statistics, discrete and continuous variables, and various types of graphs. The document also includes examples and exercises on bar graphs, pie charts, and line graphs, as well as an explanation of the inverse square law and data plotting using log graphs.
Typology: Slides
2011/2012
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Stochastic Methods
Topic: Introductory Statistics
Dr. Nasir M Mirza
Computational Physics Computational Physics
Email: [email protected]
Docsity.com
Lecture Four :
Introductory Statistics
Monte Carlo Methods
Monte Carlo Methods
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Fundamentals Inductive Statistics:
The statistics that deals with conditions
under which certain inferences are valid, is called āInductivestatisticsā. Deductive Statistics:
It is to analyze and describe a given
group without drawing conclusions. TYPES OF VARIABLES Discrete Variable:
A variable having discrete data values is
discrete variable. For example; x = 0, 1, 2,... , Continuous variable:^ Continuous variable:
A variable that can have continuous data
values. For example, the x = age of an individual.
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Graphs: bar graphs
africa
asia
europe
north america
oceania
south america
russia
0
5
10
15
20
25
30
Area (millions of square Kilometers)
Continent
area
africa
asia
europe
north america
oceania
south america
russia
Table showing area of various continents of the world.
This figure shows a bargraph in which bars arehorizontal instead ofvertical.
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Graphs: bar graphs
Continent
area
africa
asia
europe
north america
oceania
south america
russia
Table showing area of various continents of the world.
This figure shows a piegraph or pie chart invertical form.
russia20.5 (15%)
s. america17.9 (13%)
oceania8.5 (6.4%)
n. america24.3 (18%)
europe4.9 (3.7%)
asia26.9 (20%)
africa30.3 (23%)
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Graphs: bar graphs
time
Value
Table showing area of various continents of the world.
This figure shows a line graph.
0
2
4
6
8
10
0
80 60 40 20
140 120 100
number of tonnes
time (year)
scales
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Semi -
Log Graph Paper
1 10 100
0
1
2
3
4
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0
50
100
150
200
1
10
100
1000 Count Rate
Time (min)
data value
Time(min)
R
(counts/s)
4
392.
36
161.
68
65.
100
26.
132
10.
164
4.
196
1.
218
1
Example: Radioactive decay
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Data Plotting
ln(
)
ln(
)
2 ln( )
X
A
r
y
c
mx
=
Ī
ā
=
&
1
1 0
1 00
1
1 0
1 0 0 Exposure rate
D is ta n c e , r
d a ta v a lu e
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Frequency Distributions Raw Data:
It is the collected data that has not been organized yet.
Arrays:
An array is an arrangement of the raw numerical data in ascending
or descending order of magnitude. Range of the data
is the difference between maximum and minimum of data.
Weight
(kg)
Number of
students
Total:
Data is often distributed into classesor categories or bins. Number of classes
depend on user.
And to determine number ofindividuals in each class is calledclass frequency. The tabular for of data in form offrequency versus classes is calledfrequency distribution
shown here in
table.
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Histogram and Frequency Polygon
58
60
62
64
66
68
70
72
74
0
40 30 20 10
Frequency
Weight, X, (kg)
Histogram consistsof a set ofrectangles that havebases on x-axis andlength equal to classsize and areaproportional to thefrequency of class. This is shown hereas graph.
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Histogram and Frequency Polygon
60
62
64
66
68
70
72
5 0 45 40 35 30 25 20 15 10
Frequency
Weight, X, (kg)
Frequency Polygonconsists of a linegraph of the classfrequency (f) plottedagainst the classmark (X). This is shown here.
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Mean or Average Value:
The Arithmetic Mean: It is the mean of a set of N numbers say X
1
, X
2
, X
3
,... X
N
and is given as
The Mean: If the numbers X
1
, X
2
, X
3
,... X
N
occur with f
1
, f
2
, f
3
,... , f
N
times respectively
then the mean or average is given as
N
X
N
X X X X X X
N i
i
N
ā
= = + + + + =
=
<
1
3
2
1
L
ā
ā
= = = + + + +
=
=
<
N i
i
N i
i
i
N
N
N
f
X f f f f f
X f X f X f X f X X
1
1
3
2
1
3 3 2 2 1 1
L
L
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Median and Mode Median For a set of numbers arranged in order of magnitude, it is eithermiddle value or the AM of two middle values. Example:
The set of numbers 3,4,4,6,8,8,8 and 10 has median
6. Mode The mode of a set of numbers is the value that is repeatedmaximum times. Example:
The set 2, 2, 5, 7, 9, 9, 9, 10, 11, 12
and
18 has
mode 9.
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