FUNDAMENTALS OF STATISTICS
By: GUPTA,SC
Material type:
TextPublisher: HIMALAYA PUBLISHING HOUSE ISBN: 978-9350517697Subject(s): MEANING AND SCOPE ORIGIN AND DEVELOPMENT OF STATISTICS DEFINITION OF STATISTICS IMPORTANCE AND SCOPE OF STATISTICS LIMITATIONS OF STATISTICS DISTRUST OF STATISTICS EXERCISE COLLECTION OF DATA INTRODUCTION Objectives and Scope of the Enquiry. Statistical Units to be Used. Sources of Information (Data). Methods of Data Collection. Degree of Accuracy Aimed at in the Final Results. Type of Enquiry. PRIMARY AND SECONDARY DATA Choice between Primary and Secondary Data. METHODS OF COLLECTING PRIMARY DATA Direct Personal Investigation. Indirect Oral Investigation. Information Received Through Local Agencies. Mailed Questionnaire Method. Schedules Sent Through Enumerators. DRAFTING OR FRAMING THE QUESTIONNAIRE SOURCES OF SECONDARY DATA Published Sources. Unpublished Sources. PRECAUTIONS IN THE USE OF SECONDARY DATA . CLASSIFICATION AND TABULATION INTRODUCTION — ORGANISATION OF DATA CLASSIFICATION Functions of Classification. Rules for Classification. Bases of Classification. FREQUENCY DISTRIBUTION Array Discrete or Ungrouped Frequency Distribution. Grouped Frequency Distribution. Continuous Frequency Distribution. BASIC PRINCIPLES FOR FORMING A GROUPED FREQUENCY DISTRIBUTION Types of Classes. Number of Classes. Size of Class Intervals. Types of Class Intervals. CUMULATIVE FREQUENCY DISTRIBUTION Less Than Cumulative Frequency. More Than Cumulative Frequency. BIVARIATE FREQUENCY DISTRIBUTION. TABULATION — MEANING AND IMPORTANCE Parts of a Table. Requisites of a Good Table. . DIAGRAMMATIC AND GRAPHIC REPRESENTATION INTRODUCTION DIFFERENCE BETWEEN DIAGRAMS AND GRAPHS DIAGRAMMATIC PRESENTATION General Rules for Constructing Diagrams. Types of Diagrams. One-dimensional Diagrams. Two-dimensional Diagrams. Three-Dimensional Diagrams. Pictograms Cartograms Choice of a Diagram. . GRAPHIC REPRESENTATION OF DATA Technique of Construction of Graphs. General Rules for Graphing. Graphs of Frequency Distributions. Graphs of Time Series or Historigrams. Semi-Logarithmic Line Graphs or Ratio Charts. LLMITATIONS OF DIAGRAMS AND GRAPHS. -AVERAGES OR MEASURES OF CENTRAL TENDENCY .INTRODUCTION REQUISITES OF A GOOD AVERAGE OR MEASURE OF CENTRAL TENDENCY VARIOUS MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN Step Deviation Method for Computing Arithmetic Mean. Mathematical Properties of Arithmetic Mean. Merits and Demerits of Arithmetic Mean. WEIGHTED ARITHMETIC MEAN .MEDIAN Calculation of Median. Merits and Demerits of Median. Partition Values. Graphic Method of Locating Partition Values. . MODE Computation of Mode. Merits and Demerits of Mode. Graphic Location of Mode. EMPIRICAL RELATION BETWEEN MEAN (M), MEDIAN (Md) AND MODE.GEOMETRIC MEAN Merits and Demerits of Geometric Mean. Compound Interest Formula. Average Rate of a Variable Which Increases by Different Rates at Different Periods. Wrong Observations and Geometric Mean. Weighted Geometric Mean. HARMONIC MEAN Merits and Demerits of Harmonic Mean. Weighted Harmonic Mean. RELATION BETWEEN ARITHMETIC MEAN, GEOMETRIC MEAN AND HARMONIC MEAN SELECTION OF AN AVERAGE LIMITATIONS OF AVERAGES. MEASURES OF DISPERSION INTRODUCTION AND MEANING Objectives or Significance of the Measures of Dispersion. CHARACTERISTICS FOR AN IDEAL MEASURE OF DISPERSION ABSOLUTE AND RELATIVE MEASURES OF DISPERSION MEASURES OF DISPERSION . RANGE Merits and Demerits of Range. Uses.•QUARTILE DEVIATION OR SEMI INTER-QUARTILE RANGE Merits and Demerits of Quartile Deviation. PERCENTILE RANGE . MEAN DEVIATION OR AVERAGE DEVIATION Computation of Mean Deviation. Short-cut Method of Computing Mean Deviation. Merits and Demerits of Mean Deviation. Uses. Relative Measure of Mean Deviation. . STANDARD DEVIATION Mathematical Properties of Standard Deviation. Merits and Demerits of Standard Deviation Variance and Mean Square Deviation. Different Formulae for Calculating Variance. INTERPRETING STANDARD DEVIATION . Empirical Rule... Chebyshev's Theorem.. Z-scores or Standard Scores. . STANDARD DEVIATION OF THE COMBINED SERIES COEFFICIENT OF VARIATION GINNI'S MEAN DIFFERENCE . Standard Deviation in Terms of Mutual Differences. RELATIONS BETWEEN VARIOUS MEASURES OF DISPERSION . LORENZ CURVE. GINNI'S COEFFICIENT OF CONCENTRATION. . SKEWNESS, MOMENTS AND KURTOSIS INTRODUCTION SKEWNESS • Measures of Skewness. • Karl Pearson's Coefficient of Skewness. . • Bowley's Coefficient of Skewness. • . Coefficient of Skewness based on Moments. MOMENTS . Moments about Mean. Moments about Arbitrary Point A. • Relation between Moments about Mean and Moments about Arbitrary Point 'A'. • Effect of Change of Origin and Scale on Moments about Mean. • Sheppard's Correction for Moments. . Charlier Checks. KARL PEARSON'S BETA (13) AND GAMMA (y) COEFFICIENTS BASED ON MOMENTS COEFFICIENT OF SKEWNESS BASED ON MOMENTS KURTOSIS. CORRELATION ANALYSIS. Types of Correlation • Correlation and Causation. METHODS OF STUDYING CORRELATION SCATTER DIAGRAM METHOD EXERCISE 84 KARL PEARSON'S COEFFICIENT OF CORRELATION (COVARIANCE METHOD) • Properties of Correlation Coefficient . Assumptions Underlying Karl Pearson's Correlation Coefficient. Interpretation of r. PROBABLE ERROR CORRELATION IN BIVARIATE FREQUENCY TABLE RANK CORRELATION METHOD • Limits for p. • Computation of Rank Correlation Coefficient (p). • Remarks on Spearman's Rank Correlation Coefficient METHOD OF CONCURRENT DEVIATIONS COEFFICIENT OF DETERMINATION LAG AND LEAD CORRELATION LINEAR REGRESSION ANALYSIS INTRODUCTION LINEAR AND NON-LINEAR REGRESSION LINES OF REGRESSION. COST OF LIVING INDEX NUMBER . Main Steps in the Construction of Cost of Living Index Numbers _ Construction of Cost of Living Index Numbers. . Uses of Cost of Living Index Numbers. LIMITATIONS OF INDEX NUMBERS TIME SERIES ANALYSIS INTRODUCTION COMPONENTS OF A TIME SERIES Secular Trend. Short-Term Variations. Random or Irregular Variations. ANALYSIS OF TIME SERIES MATHEMATICAL MODELS FOR TIME SERIES MEASUREMENT OF TREND Graphic or Free Hand Curve Fitting Method. Method of Semi-Averages. Method of Curve Fitting by the Principle of Least Squares. Conversion of Trend Equation. Selection of the Type of Trend. Method of Moving Averages. MEASUREMENT OF SEASONAL VARIATIONS Method of Simple Averages. Ratio to Trend Method. 'Ratio to Moving Average' Method. Method of Link Relatives. Deseasonalisation of Data. MEASUREMENT OF CYCLICAL VARIATIONS MEASUREMENT OF IRREGULAR VARIATIONS TIME SERIES ANALYSIS IN FORECASTING THEORY OF PROBABILITY INTRODUCTION SHORT HISTORY TERMINOLOGY MATHEMATICAL PRELIMINARIES Set Theory. Permutation and Combination. MATHEMATICAL OR CLASSICAL OR 'A PRIORI' PROBABILITY STATISTICAL OR EMPIRICAL. AXIOMATIC PROBABILITY ADDITION THEOREM OF PROBABILITY Addition Theorem of Probability for Mutually Exclusive Events. Generalisation of Addition Theorem of Probability. THEOREM OF COMPOUND PROBABILITY OR MULTIPLICATION THEOREM OF PROBABILITY Generalisation of Multiplication Theorem of Probability. Independent Events. Multiplication Theorem for Independent Events. PAIRWISE AND MUTUAL INDEPENDENCE OBJECTIVE TYPE QUESTIONS INVERSE PROBABILITY Bayes' Theorem (Rule for the Inverse Probability) RANDOM VARIABLE, PROBABILITY DISTRIBUTIONS AND MATHEMATICAL • RANDOM VARIABLE PROBABILITY DISTRIBUTION OF A DISCRETE RANDOM VARIABLE PROBABILITY DISTRIBUTION OF A CONTINUOUS RANDOM VARIABLE Probability Density Function (p.d.f.) of Continuous random Variable DISTRIBUTION FUNCTION OR CUMULATIVE PROBABILITY FUNCTION MOMENTS .MATHEMATICAL EXPECTATION Physical Interpretation of E(X). THEOREMS ON EXPECTATION VARIANCE OF X IN TERMS OF EXPECTATION COVARIANCE IN TERMS OF EXPECTATION VARIANCE OF LINEAR COMBINATION Aliter. Proof in Terms of Expectation JOINT AND MARGINAL PROBABILITY DISTRIBUTIONS THEORETICAL DISTRIBUTIONS INTRODUCTION BINOMIAL DISTRIBUTION Probability Function of Binomial Distribution. Constants of Bionomial Distribution Mode of Binomial Distribution. Fitting of Binomial Distribution. .POISSON DISTRIBUTION (AS A LIMITING CASE OF BINOMIAL DISTRIBUTION) Utility or Importance of Poisson Distribution. Constants of Poisson distribution. SYSTEMATIC SAMPLING . Merits and Demerits CLUSTER SAMPLING MULTISTAGE SAMPLING QUOTA THEORY OF ESTIMATION AND TESTING OF HYPOTHESIS INTRODUCTION ESTIMATION THEORY Point Estimation. Unbiasedness. Consistency. Efficiency. Sufficiency. Methods of Point Estimation. SAMPLING DISTRIBUTION OF A STATISTIC Sampling Distribution of Mean. Central Limit Theorem. Sampling Distribution of Proportion. INTERVAL ESTIMATION Interval Estimation for Large Samples. Confidence Limits for Mean. Confidence Limits for Proportion. Confidence Limits for Standard Deviation. Confidence Limits for Difference of Means. Confidence Limits for Difference of Proportions. SIZE OF THE RANDOM SAMPLE FOR SPECIFIED PRECISION TESTING OF HYPOTHESIS Statistical Hypothesis - Simple and Composite. Tests of Significance. • Null Hypothesis. Alternative Hypothesis. Types of Errors in Testing of Hypothesis. Level of Significance. Critical Region. One-Tailed and Two-Tailed Tests. Critical Values or Significant Values and Critical Region. P-Value or Probability Value of Test Statistic PROCEDURE FOR TESTING OF HYPOTHESIS. LARGE SAMPLE TESTS LNTRODUCTION SAMPLING OF ATTRIBUTES. F - STATISTIC Critical Values of F-distribution. Chief Features of F= F(ri, n2) Distribution. Applications of F-distribution. F-tcst for Equality of Population Variances. Other Uses of F-distribution. RELATION BETWEEN t, F AND x2 DISTRIBUTIONS. .INTRODUCTION Assumptions. Uses of Interpolation. METHODS OF INTERPOLATION GRAPHIC METHOD ALGEBRAIC METHOD METHOD OF PARABOLIC CURVE FITTING METHOD OF FINITE DIFFERENCES NEWTON'S FORWARD DIFFERENCE FORMULA NEWTON'S BACKWARD DIFFERENCE FORMULA . BINOMIAL EXPANSION METHOD FOR INTERPOLATING MISSING VALUES . INTERPOLATION WITH ARGUMENTS AT UNEQUAL INTERVALS DIVIDED DIFFERENCES Newton's Divided Difference Formula. LAGRANGE'S FORMULA INVERSE INTERPOLATION STATISTICAL QUALITY CONTROL INTRODUCTION Chance and Assignable Causes of Variation. Uses of SQC. PROC
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Reference Books
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MIIMLIBRARY | RACK -REF 2 | 519.5 (Browse shelf) | Not for loan | 2597 |
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