Statistics and Mathematics Lectures
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I Statistics
1
Preliminary Concepts
1.1
Statistics: What & How
1.2
Topics
1.3
What is statistics?
1.4
How Statistics works?
1.5
Probability and Statistics
1.6
Application of Statistics
1.7
Examples
1.8
Chapter Overview
1.9
Definition
1.10
Mechanism
1.11
Population and Sample
1.12
Variable and Constant
1.13
Types of Variable
1.14
Univariate, Multivariate
1.15
Scale of Measurement
1.16
Examples
1.17
Another Example
1.18
Operation with scales
1.19
Shifting origin and scale
1.20
Use of Summation sign
1.21
Theorems
1.22
Quick tips
1.23
Example
1.24
Textbook Exercise -01
1.25
Exercises
1.26
Creative Questions
2
Collection, Presentation, and Organization of Data
2.1
Types of Data
2.2
Sources of Data
2.3
Method of Data Collection
2.4
Sources of Secondary Data
2.5
Disadvantages of Secondary Data
2.6
Tabluation
2.7
Data Classification
2.8
Example
2.9
Histogram
2.10
Histogram Intervals
2.11
Stem and Leaf
2.12
How to interpret cf and rf
2.13
What Ogives tell us
2.14
Bar vs Pie
2.15
Choose Diagram
2.16
Bar Diagram vs Histogram
3
Measures of Central Tendency
3.1
What is Central Tendency?
3.2
Criteria for a Good Measure of Central Tendency
3.3
Measures (Averages)
3.4
AM
3.5
Find AM
3.6
Mean Using Frequency
3.7
Freuency vs Weight
3.8
Shortcut Method for AM
3.9
Shortcut Method Formula
3.10
Properties of AM
3.11
(Dis)advantages of AM
3.12
Geometric Mean (GM)
3.13
Concept of Logarithm
3.14
GM Easier Formula
3.15
Calculate GM
3.16
(Dis)advantages of GM
3.17
Story of Oil Scam
3.18
Harmonic Mean
3.19
Why and When HM
3.20
Wighted AM vs Weighted HM
3.21
HM Example 2
3.22
Quadratic Mean
3.23
Partition Values
3.24
Find medians
3.25
Dis(advantages) of Median
3.26
Quartiles, Deciles, and Percentiles
3.27
General Formula for Partition Values
3.28
Find Deciles and Percentiles
3.29
Averages from Grouped Data
3.30
Partition Values from Graph
3.31
Comparison of Averages
3.32
When AM = GM = HM
3.33
Theorems
3.34
Example Problems
4
Measures of Dispersion
5
Moments, Skewness, and Kurtosis
5.1
Central Moments
5.2
Raw Moments
6
Correlation & Regression
6.1
Why This Chapter is Important
6.2
Scatter Plot
6.3
Sequence
6.4
Correlation
6.5
Scatter Plot And Correlation
6.6
r: Estimating Mechanism
6.7
Example of r
6.8
Features of r
6.9
Rank Correlation
6.10
Linear Equation/ Straight Lines
6.11
Purity of Coefficients
7
Time Series
7.1
What is Time Series Data?
7.2
Components of Time Series
7.3
Uses
7.4
Symbols
7.5
Models
7.6
Comparison of Models
7.7
Measuring Trend
7.8
Graphical/Free-hand Method
7.9
Sem-average
7.10
Moving Average
II Probability
8
Introduction to Probability
8.1
Important concepts
8.2
Three Definitions
8.2.1
Classical
8.2.2
Relative frequency
8.2.3
Axiomatic
8.3
Permutaion vs Combination
8.4
Dependency and Mutual Exclusivity
8.5
Types of Problems
8.6
Miscellaneous
8.6.1
Misc Problem #01
8.6.2
Misc Problem #02
8.6.3
Misc Problem #03
8.7
Coin And Die Problem
8.7.1
Tossing A Coing Twice
8.7.2
Flipping A Coin Thrice
8.7.3
Flinging Two Dice at Once
8.8
Playing Card
8.8.1
Concepts (Playing Card)
8.8.2
Card Problem #01
8.8.3
Card Problem #02
8.8.4
Card Problem #03
8.8.5
Card Problem #04
8.8.6
Card Problem #05
8.9
Box
8.9.1
Box Problem #01
8.9.2
Box Problem #02
8.9.3
Box Problem #02
8.10
Conditional Probability
8.10.1
Conditional Formula
8.10.2
Conditional Problem # 01
8.10.3
Conditional Problem # 02
8.10.4
Conditional Problem # 03
8.10.5
Conditional Problem # 04
8.11
Set Theoretic
8.11.1
Concept
8.11.2
Set Problem # 01
8.11.3
Set Problem # 02
8.11.4
Set Problem # 03
8.11.5
Set problem # 04
8.11.6
Set problem # 05
8.11.7
Set problem # 06
8.11.8
Set problem # 07
8.11.9
Set problem # 08
Appendix
A
Permutation
A.1
Arranging Subset
A.2
What is 0!
A.3
Rule of Counting
A.4
Example of counting rule
A.5
Exercises of permutation
A.6
Without Changing Position
A.7
Specific Word at First/Last
A.8
Even/Odd/middle positions
A.9
Digit Problems
A.10
Summation Basics
A.11
Sum-Average
A.12
Specific Items Apart/First/Last
A.13
Arranging in Seats/Positions
A.14
Circular Combination
B
Combination
B.1
Concept
B.2
Formulae And Notation
B.3
Expaniosn of
\(^nC_r\)
B.4
Theoretical Problems
B.5
Repeated Items
B.6
Repeated Items (Ctd.)
B.7
Conditional Capacity
B.8
Always In(Ex)cluding
B.9
Always In(Ex)cluding Problems
B.10
At least one
B.11
At least one (Problems)
III Presentations
Presentations
How to Use
Statistics
Mathematics
Questions
Published with bookdown
Statistics and Mathematics Lectures
5.2
Raw Moments
\(\mu_r=\frac{\sum(x_i-a)^r}{n}\)
; a is arbitrary number