Statistical methods /
N.G. Das
- New Delhi : Tata Mcgraw hill , 2009.
- 905 p.
- V. 1& 2 .
1. Collection of Data: Classification and Tabulation 1.1 Meaning of 'Statistics' 1 1.2 Variable and Attribute 3 1.3 Primary Data and Secondary Data 4 1.4 Population (or Universe) and Sample 6 1.5 Complete Enumeration (or Census) and Sample Survey 7 1.6 Statistical Enquiry 8 1.7 Useful Terms 11 1.8 Classification 14 1.9 Tabulation 14 1.10 Mechanical Tabulation 20 Exercises 21 Answers 24 2. Charts and Diagrams 2.1 Objects of Diagrammatic Representation 27 2.2 Types of Charts and Diagrams 27 Exercises 41 Answers 43 3. Useful Mathematical Devices 3.1 Rounding of Numbers 44 3.2 Absolute, Relative and Percentage Errors 44 3.3 Significant Figures 45 3.4 Some Short Processes of Calculation 46 3.5 Roots and Reciprocals Expressed as Power 49 3.6 Logarithm 49 3.7 A.P. Series and G.P. Series 54 3.8 Sum and Sum of the Squares of Numbers 55 3.9 Simple Interest Law and Compound Interest Law 55 3.10 Permutation and Combination 56 3.11 Binomial Series and Binomial Coefficients 56 3.12 Inequalities 57 3.13 Concept of'Function' 57 3.14 Polynomial 58 3.15 Sigma (E) Notation 58 3.16 Simple Interpolation 63 4. Frequency Distribution 4.1 Observation, Frequency 66 4.2 Simple Series (or Ungrouped Data) and Frequency Distribution 66 4.3 Useful Terms Associated with Grouped Frequency Distributions 69 4.4 Construction of Frequency Distribution 78 4.5 Cumulative Frequency Distribution 81 4.6 Relative Frequency Distribution 87 4.7 Diagrammatic Representation of Frequency Distributions 87 4.8 Frequency Curve 95 Exercises 97 Answers 99 5. Measures of Central Tendency 5.1 Averages or Measures of Central Tendency lOI 5.2 Arithmetic Mean (A.M.) 106 5.3 Important Properties of A.M. 110 5.4 Simplified Calculation for A.M. 115 5.5 Mean of Composite Group 124 5.6 Geometric Mean (G.M.) 126 5.7 Properties of G.M. 127 5.8 Harmonic Mean (H.M.) 133 5.9 Advantages and Disadvantages of A.M., G.M., H.M. 135 5.10 Relations between A.M., G.M., H.M. 137 5.11 Median 140 5.12 Calculation of Median 140 5.13 Advantages and Disadvantages of Median 141 5.14 Mode 152 5.15 Calculation of Mode 152 5.16 Advantages and Disadvantages of Mode 153 5.17 Relation between Mean, Median, Mode 157 5.18 Partition Values—Quartiles, Deciles, Percentiles 157 5.19 Calculation of Partition Values 158 Exercises 166 Answers 173 6. Measures of Dispersion 6.1 Meaning and Necessity of 'Measures of Dispersion' 175 6.2 Range 179 6.3 Quartile Deviation (or Semi-interquartile Range) 180 6.4 Mean Deviation (or Mean Absolute Deviation) 182 6.5 Standard Deviation (S.D.) 184 6.6 Important Properties of S.D. 185 6.7 Calculation of Standard Deviation (s) 194 6.8 S.D. of Composite Group 203 6.9 Relation between S.D. and Other Measures 208 6.10 Relative Measures of Dispersion 209 6. 1 I I i'l lMl/ ( "lll\ C J " lixmnrs 21" .4/jvui/^ 22.^ 7. Moments, Skewnes>s and Kiirtosi.s 7 I McimcntN 22-4 7.2 Relation bctuccn CVnir.il aiul Noiv ccniral MomctUs 22S 12 Beia cocllk icnis ami (iainina'CoelfK ienis 22^ 7 4 Sianilarili/cd Variable 2Mi 1.2 Motneiiis of iTeqiiency Disiribulions 220 10 Sbeppard's CmreebtMi Ita brmis due u> (iroupmg 222 1 1 Ske\MK*vs 222 7.x Kurtosis 240 Excrcisv\ 24 / Answers 244 8. Curve Fitting and Method of I.east Squares X.I Curve bitting 245 X.2 Straight Line and Parabola 240 X.3 l-ree hand Method of Curve r-itting 240 X.4 Method of I-ea.st Squares 240 8.5 Fitting Straight Line 25/ 8.6 Simplified Caleulations 25/ 8.7 Fitting Parabola 250 8.8 Fitting F.\ponential and CJeometric Curves 202 Exercises 205 Answers 207 Mathematical Note 207 9. Correlation and Regression 9.1 Concepts of'Correlation'and'Regression' 260 9.2 Bivariate Data 260 9.3 Bivariate Frequency Distribution 270 9.4 Scatter Diagram 272 9.5 Correlation 275 9.6 Covariance 275 9.7 Correlation Coefficient (; ) 276 9.8 Properties of Correlation Coefficient 277 9.9 Calculation of r 277 9.10 Interpretation and Use of r 2H5 9.11 Variance of the Sum (Difference) of Two Series 2H6 9.12 Regression 290 9.13 Properties of Linear Regression 29/ 9.14 Explained Variation and Unexplained Variation 301 9.15 Regression Curve in Bivariate Frequency Distribution 303 9.16 Rank Correlation 304 9.17 Multiple Correlation and Partial Correlation 308 Exercises 311 Answers 316 10. Interpolation 10.1 Introduction 318 10.2 Finite Differences: D and E Operators 318 10.3 Differences of a Polynomial Function 322 10.4 Newton's Forward Interpolation Formula 326 10.5 Newton's Backward Interpolation Formula 329 10.6 Central Difference Formulae-Stirling's and Bessel's 332 10.7 Lagrange's Interpolation Formula 333 10.8 Inverse Interpolation 335 11. Theory of Probability 11.1 Introduction 343 11.2 Random Experiment, Outcome, Event 343 11.3 Important Terminology 347 11.4 Techniques of Counting 349 11.5 Classical (or 'a Priori') Definition of Probability 351 ri .6 Theorems of Probability 362 11.7 Drawing without Replacement 373 11.8 Repeated Trials—Drawing with Replacement 377 11.9 Bayes' Theorem 379 11.10 Mathematical Expectation 383 11.11 Other Approaches to Probability Theory 387 11.12 Set Theory 388 11.13 Set and Probability 392 11.14 Axioms of Probability 396 11.15 Finite Probability Space and Assignment of Probabilities 398 11.16 Finite Equiprobable Sample Space and Classical Definition 399 11.17 Conditional Probability 401 11.18 Independent Events 402 11.19 Random Variable 406 11.20 Cumulative Distribution Function (C.D.F.) 410 11.21 Joint Distribution of Two Variables (Discrete) 413 Exercises 415 Answers 425 12. Theoretical Distiibutions-Binoinial, Poisson, Normal 12.1 Random Variable and Probability Distribution 426 12.2 Discrete Probability Distribution 426 12.3 Expectation.s—Mean, Variance, Moments (Discrete Distribution) 429 12.4 Uniform Distribution (Discrete) 432 12.5 Binomial Distribution 433 12.6 Poisson Distribution 441 IfJL 7 "" Approvmiation u» Hinointal Disirilnilmn 44^ I2.S n\pcii!c»>nicliic 1 )isirihiiliiMJ 447 12,'' Miilimoini.il Disiribuiioii 2 10 Dismbulion nl Iwi* \an;ibk's 4>l 12 1 1 ( ontiiuioiis Probabilil> Distnbulinn 4ft5 2.12 I■mtoriii Dislnbiuiiin (('oniimioiis) 467 2 ! ^ Noimal Distnbiilion 4fhS 2. 14 Norin.il Appro\imatii)n in l^inntniai (PoissoiO 475 2. 15 ("ntiirni I.irnii Ihcoivin 47" I-.\tni\t"t 477 Answers 4Sft 13. Sampling Theory I .VI Meaning aiul Objecls ol 'Sampling" 4cVI .V2 Sampling Faror and BIAs 4^)0 I .V.^ lypes ol" Sampling 492 I .V4 Mcihod ol' Drawing Random Sample 495 I.V5 Sampling Distribution 499 I.V6 Two Impoitant Sampling Distribution (l.argc Sample) 501 I.V7 Slaiuiard f'irror (S.IV) 501 I .V7A ITobable lirror (l^.li.} 5/6 I3.S Distributions Used in Sampling Theory 5/7 A.ve/c/.ve.v 525 Answers 526 14. Estimation and Test of Significance 14.1 Introduction 52H 14.2 Theory ol" Kstimation 52H 14.3 Point Estimation—Criteria for Good Estimators 52H 14.4 Methods of Point Estimation 554 14.5 Interval Estimation 557 14.6 Theory of Test of Significance 546 14.7 Large Sample Te.sts 554 14.8 Small Sample Tests 572 14.9 Tests for Correlation Coefficient 5H7 Exercises 601 Answers 611 15. Analysis of Variance 15. 1 Introduction 6/5 15.2 Different Sources of Variation 615 15.3 Technique in One-way Classified Data 616 15.4 Steps in Computation (One-way Cla.ssified Data) 618 15.5 Locating Unequal Pairs of Means 619 15.6 Technique in Two-way Classified Data 623 15.7 Steps in Computation (Two-way Classified Data) 625 Exercises 627 Answers 630 16. Time Series 16.1 Meaning and Necessity of'Time Series Analysis' 632 16.2 Components of Time Series 632 16.3 Adjustments to Time Series Data 634 16.4 Secular Trend 635 16.5 Measurement of Trend 635 16.6 Monthly Trend from Annual Data 653 16.7 Seasonal Variation 658 16.8 Measurement of Seasonal Variation 661 16.9 Cyclical Fluctuation 672 16.10 Business Forecasting 673 16.11 Exponential Smoothing 674 Exercises 676 Answers 683 17. Index Numbers 17.1 Meaning of'Index Number' 686 17.2 Problems in Construction of Index Numbers 688 17.3 Methods of Construction of Index Numbers 689 17.4 Quantity Index Number 701 17.5 Tests of Index Numbers 706 17.6 Chain Base Method 713 n.l Cost of Living Index Numbers 715 17.8 Bias in Laspeyres' and Paasche's Formulae for C.L.I. 724 17.9 Base Shifting, Splicing and Deflation 726 17.10 Errors in Index Numbers 730 Exercises 730 Answers 741 18. Vital Statistics 18.1 Introduction 743 18.2 Crude Death Rate 744 18.3 Specific Death Rate 744 18.4 Standardised Death Rate 745 18.5 Life Table 748 18.6 Crude Birth Rate 752 18.7 General Fertility Rate 752 18.8 Age-specific Fertility Rate 753 18.9 Total Fertility Rate 753 18.10 Vital Index 753 18.11 Gross Reproduction Rate 754 18.12 Net Reproduction Rate 754 Exercises 758 Answers 763 19. Statistical Quality Control 19.1 Introduction 765 19.2 Chance Causes and Assignable Causes 766 19.3 Control Chart—How It Works 766 19.4 Control Charts for Variables and Attributes 768 19.5 Formulae for Central Line and Control Limits 769 19.6 Sampling Inspection 777 19.7 Single and Double Sampling Inspection Plans 778 19.8 Important Terms used in Sampling Inspection 779 Exercises 780 Answers 783