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STATISTICAL METHODS I

STATISTICAL METHODS I


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माहिती

प्रस्तावना

1. Data Condensation and Graphical Methods
    Introduction
1. Attributes and Variables
2. Classification
2.1 Frequency Distribution
2.2 Cumulative Frequency Distribution
2.3 Relative Frequency Distribution
3. Stem and Leaf Chart
4. Graphical Presentation of Frequency Distribution or Diagrams
4.1 Simple Bar Diagram
4.2 Sub-Divided Bar Diagram
4.3 Pie Diagram
4.4 Choice of a Suitable Diagram
4.5 Less than and More than Type Ogive curves
2. Review/Revision of Descriptive Statistics
1. Measure of Central Tendency
1.1 Arithmetic Mean
1.2 Weighted Arithmetic Mean
1.3 Median
1.4 Mode
1.5 Appropriate Choice of an Average
2. Partition Values
2.1 Quartiles
2.2 Deciles
2.3 Percentiles
2.4 Percentile Rank
2.5 Box Plot
3. Measure of Dispersion
3.1 Quartile Deviation
3.2 Variance and Standard Deviation
3.3 Coefficient of Variation
3. Moments
1. Introduction
2. Raw Moments (About Origin)
3. Central Moments
4. Moments about an Arbitrary Value ‘A’
5. Relation between Raw and Central Moments
6. Properties of Central Moments
4. Measures of Skewness and Kurtosis
1. Introduction
2. Concept of Symmetric Distribution, Skewness
2.1 Skewness
2.2 Positively Skewed Distribution
2.3 Negatively Skewed Distributions
2.4 Empirical Relationship among Mean, Median and Mode
3. Measures of Skewness
3.1 Pearson’s Measure
3.2 Bowley’s Measure
3.3 Karl Pearson’s b1, g1 Coefficients
4. Kurtosis
4.1 Measure of Kurtosis11
5. Choice of a Measure of Skewness and Kurtosis
    Solved Examples 12
5. Discrete Random Variable
1. Introduction
2. Random Variable and Discrete Random Variable
3. Probability Mass Function
3.1 Distribution Function or Cumulative Probability Function
3.2 Properties of Distribution Function
4. Expectation
4.1 Expectation of a Function of a Discrete Random Variable
4.2 Theorems on Expectation
5. Variance
6. Determination of Median and Mode using p.m.f.
6. Standard Discrete Distributions
1. Introduction
2. Discrete Uniform Distribution
2.1 Mean and Variance of Uniform Distribution
3. Bernoulli Distribution
3.1 Mean and Variance of Bernoulli Distribution
3.2 Additive property of Bernoulli Distribution
4. Binomial Distribution
4.1 Mean and Variance of Binomial Distribution
4.2 Additive Property of Binomial Distribution
4.3 Recurrence Relation for Binomial Probabilities
4.4 Fitting of Binomial Distribution
     Solved Examples
5. Geometric Distribution
5.1 Mean and Variance
     Solved Problems
6. Poisson Distribution
6.1 Mean and Variance
6.2 Mode of the Poisson Distribution
6.3 Additive Property of Poisson Distribution
6.4 Poisson Distribution as a Limiting Form of Binomial Distribution
6.5 Recurrence Relation for Poisson Probabilities
6.6 Fitting of Poisson Distribution
     Solved Problems
7. Correlation
1. Introduction
2. Bivariate Data
3. Correlation
3.1 Positive and Negative Correlation
4. Scatter Diagram Method
5. Karl Pearson’s Coefficient Of Correlation (r)
5.1 Properties of Correlation Coefficient
5.2 Interpretation of ‘r’
6. Coefficient of Determination (r2)
7. Auto-Correlation upto Lags 2
8. Regression (For Ungrouped Data)
1. Introduction
2. Linear Regression
3. Fitting of Straight Line Using Least Square Method
3.1 Derivation of Line of Regression of Y on X
3.2 Line of Regression of X on Y
4. Properties of Regression Coefficients
5. Non–Linear Regression
5.1 Fitting of Second Degree Parabola
5.2 Fitting of Growth Curve Models
6. Residual Plot, Mean Residual Sum and Squares (m.s.s.)
9. Multiple and Partial Correlation and Regression (For Trivariate Data)
1. Introduction
2. Notation
3. Yule’s Notation
4. Fitting of Multiple Regression Plane
5. Partial Regression Coefficient, Interpretation
   Solved Examples
6. Multiple Correlation Coefficient
7. Partial Correlation Coefficient
10. Time Series
1. Introduction
2. Meaning and Utility
3. Components of Time Series
3.1 Secular Trend (T)
3.2 Seasonal Variations (S)
3.3 Cyclical Variations (C)
3.4 Irregular or Random Variations (I)
4. Additive and Multiplicative Models
4.1 Additive Model
4.2 Multiplicative Model
5. Methods of Estimating Trend
5.1 Moving Average Method
5.2 Least Squares Method
5.3 Exponential Smoothing Method
6. Elimination of Trend Using Additive and Multiplicative Models
7. Simple Time Series Models

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STATISTICAL METHODS I

STATISTICAL METHODS I

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