Schaum's outline of theory and problems of statistics

Contents......Page 15
Variables: Discrete and Continuous......Page 25
Scientific Notation......Page 26
Computations......Page 27
Graphs......Page 28
Inequalities......Page 29
Logarithms......Page 30
Logarithmic Equations......Page 31
Frequency Distributions......Page 61
General Rules for Forming Frequency Distributions......Page 62
Relative-Frequency Distributions......Page 63
Relative Cumulative-Frequency Distributions and Percentage Ogives......Page 64
Types of Frequency Curves......Page 65
Summation Notation......Page 85
The Weighted Arithmetic Mean......Page 86
The Arithmetic Mean Computed from Grouped Data......Page 87
The Empirical Relation Between the Mean, Median, and Mode......Page 88
The Harmonic Mean H......Page 89
Quartiles, Deciles, and Percentiles......Page 90
Software and Measures of Central Tendency......Page 91
The Mean Deviation......Page 119
The Standard Deviation......Page 120
Short Methods for Computing the Standard Deviation......Page 121
Properties of the Standard Deviation......Page 122
Charlier’s Check......Page 123
Absolute and Relative Dispersion; Coefficient of Variation......Page 124
Software and Measures of Dispersion......Page 125
Moments for Grouped Data......Page 147
Moments in Dimensionless Form......Page 148
Kurtosis......Page 149
Software Computation of Skewness and Kurtosis......Page 150
Definitions of Probability......Page 163
Conditional Probability; Independent and Dependent Events......Page 164
Mutually Exclusive Events......Page 165
Probability Distributions......Page 166
Relation Between Population, Sample Mean, and Variance......Page 168
Combinatorial Analysis......Page 169
Euler or Venn Diagrams and Probability......Page 170
The Binomial Distribution......Page 196
The Normal Distribution......Page 197
Relation Between the Binomial and Normal Distributions......Page 198
The Poisson Distribution......Page 199
Relation Between the Binomial and Poisson Distributions......Page 200
Fitting Theoretical Distributions to Sample Frequency Distributions......Page 201
Random Samples and Random Numbers......Page 227
Sampling Distribution of Means......Page 228
Sampling Distributions of Differences and Sums......Page 229
Software Demonstration of Elementary Sampling Theory......Page 231
Unbiased Estimates......Page 251
Confidence-Interval Estimates of Population Parameters......Page 252
Probable Error......Page 254
Statistical Hypotheses......Page 269
Tests Involving Normal Distributions......Page 270
Two-Tailed and One-Tailed Tests......Page 271
p-Values for Hypotheses Tests......Page 272
Tests Involving Sample Differences......Page 273
Tests Involving Binomial Distributions......Page 274
Student’s t Distribution......Page 299
Confidence Intervals......Page 300
The Chi-Square Distribution......Page 301
Degrees of Freedom......Page 302
The F Distribution......Page 303
Definition of χ[sup(2)]......Page 318
The Chi-Square Test for Goodness of Fit......Page 319
Contingency Tables......Page 320
Simple Formulas for Computing χ[sup(2)]......Page 321
Correlation of Attributes......Page 322
Additive Property of χ[sup(2)]......Page 323
Curve Fitting......Page 340
Equations of Approximating Curves......Page 341
The Straight Line......Page 342
The Least-Squares Line......Page 343
The Least-Squares Parabola......Page 344
Problems Involving More Than Two Variables......Page 345
Linear Correlation......Page 369
The Least-Squares Regression Lines......Page 370
Standard Error of Estimate......Page 371
Coefficient of Correlation......Page 372
Remarks Concerning the Correlation Coefficient......Page 373
Short Computational Formulas......Page 374
Sampling Theory of Correlation......Page 375
Sampling Theory of Regression......Page 376
Regression Equations and Regression Planes......Page 406
Regression Planes and Correlation Coefficients......Page 407
Change of Dependent Variable......Page 408
Partial Correlation......Page 409
Nonlinear Multiple Regression......Page 410
One-Way Classification, or One-Factor Experiments......Page 427
Shortcut Methods for Obtaining Variations......Page 428
Expected Values of the Variations......Page 429
Analysis-of-Variance Tables......Page 430
Two-Way Classification, or Two-Factor Experiments......Page 431
Variations for Two-Factor Experiments......Page 432
Analysis of Variance for Two-Factor Experiments......Page 433
Two-Factor Experiments with Replication......Page 434
Experimental Design......Page 436
The Sign Test......Page 470
The Mann–Whitney U Test......Page 471
The H Test Corrected for Ties......Page 472
The Runs Test for Randomness......Page 473
Spearman’s Rank Correlation......Page 474
General Discussion of Control Charts......Page 504
X-bar and R Charts......Page 505
Process Capability......Page 508
P- and NP-Charts......Page 511
Other Control Charts......Page 513
Answers to Supplementary Problems......Page 529
Appendixes......Page 583
I: Ordinates (Y) of the Standard Normal Curve at z......Page 585
II: Areas Under the Standard Normal Curve from 0 to z......Page 586
III: Percentile Values (t[sub(p)]) for Student’s t Distribution with ν Degrees of Freedom......Page 587
IV: Percentile Values (χ[sup(2)][sub(p)]) for the Chi-Square Distribution with ν Degrees of Freedom......Page 588
V: 95th Percentile Values for the F Distribution......Page 589
VI: 99th Percentile Values for the F Distribution......Page 590
VII: Four-Place Common Logarithms......Page 591
VIII: Values of e[sup(–λ)]......Page 593
IX: Random Numbers......Page 594
C......Page 595
D......Page 596
G......Page 597
N......Page 598
R......Page 599
T......Page 600
Z......Page 601