TY - BOOK AU - N. Das TI - Statistical methods SN - 9780070083271(pb) U1 - 001.422 PY - 2009/// CY - New Delhi PB - Tata Mcgraw hill N1 - 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" 4cV