CHAPTER Ⅰ THE NATURE OF STATISTICS 1
1．1 Scientific Method 1
1．2 Experimental Method 1
1．3 Statistical Method 2
1．4 Statistics 4
1．5 Preliminary Admonitions 4
1．6 Suggestions for Further Reading 6
CHAPTER Ⅱ THE MEANING OF NUMBERS 7
2．1 Accuracy of Measurement 7
2．2 Biassed and Compensating Errors 8
2．3 Significant Figures 10
2．4 Standard Notation 13
2．5 Computations with Approximate Nubmers 15
2．6 Multiplication and Division of Approximate Numbers 16
2．7 Addition and Subtraction of Approximate Numbers 18
2．8 A Horrible Example 20
2．9 Rounding Off Numbers 22
2．10 Suggestions for Further Reading 23
Exercises 24
CHAPTER Ⅲ THE FREQUENCY DISTRIBUTION 26
3．1 The Frequency Table 26
3．2 Class Limits 28
3．3 Overlapping Class Limits 32
3．4 Open-end Classes 32
3．5 Class Intervals 33
3．6 Class Marks 33
3．7 Cumulative Frequency Tables 35
3．8 Graphic Presentation：the Histogram 36
3．9 Graphic Presentation：the Frequency Polygon 37
3．10 Graphic Presentation：the Frequency Curve 38
3．11 Graphic Presentation：the Ogive 39
3．12 What to Look for in a Frequency Table 40
3．13 Common Shapes of Frequency Curves 41
3．14 Common Shapes of Ogives 43
3．15 Making a Frequency Table：How Many Classes？ 44
3．16 Making a Frequency Table：Rules of Thumb 47
3．17 Making a Frequency Table：Choosing the Class Interval 48
3．18 When to Use Unequal Class Intervals 49
3．19 How to Use Unequal Class Intervals 51
3．20 Logarithmic Frequency Classes 53
3．21 Making a Frequency Table：Locating the Class Marks 54
3．22 Summary：Directions for Making a Frequency Table 57
3．23 Suggestions for Further Reading 58
Exercises 58
CHAPTER Ⅳ MEASURES OF CENTRAL TENDENCY 61
4．1 Averages 61
4．2 The Arithmetic Mean：Ungrouped Data 61
4．3 Weighted Arithmetic Mean 63
4．4 The Median：Ungrouped Data 66
4．5 The Mode：Ungrouped Data 68
4．6 The Geometric Mean：Ungrouped Data 70
4．7 The Harmonic Mean：Ungrouped Data 71
4．8 The Quadratic Mean：Ungrouped Data 74
4．9 Quartiles，Deciles，and Percentiles：Ungrouped Data 75
4．10 Use of Quartiles，Deciles，Etc 78
4．11 Summary of Averages with Ungrouped Data 79
Exercises 80
CHAPTER Ⅴ MEASURES OF CENTRAL TENDENCY(CONTINUED) 82
5．1 Averages from Grouped Data 82
5．2 The Arithmetic Mean：Grouped Data 84
5．3 Arithmetic Mean：Short Method 87
5．4 Checking Accuracy of Computations 91
5．5 Grouping Error with the Arithmetic Mean 92
5．6 The Median：Grouped Data 93
5．7 Finding the Median from an Ogive 97
5．8 The Mode：Grouped Data 98
5．9 The Geometric Mean：Grouped Data 99
5．10 The Harmonic Mean：Grouped Data 100
5．11 The Quadratic Mean：Grouped Data 101
5．12 Quartiles，Deciles，and Percentiles：Grouped Data 103
5．13 Summary of Averages with Grouped Data 104
5．14 Characteristics of a Good Average 106
5．15 Relationships between the Averages 108
5．16 Advantages and Disadvantages of the Arithmetic Mean 109
5．17 Advantages and Disadvantages of the Median 113
5．18 Advantages and Disadvantages of the Mode 115
5．19 Advantages and Disadvantages of the Geometric Mean 116
5．20 Advantages and Disadvantages of the Harmonic Mean 120
5．21 Advantages and Disadvantages of the Quadratic Mean 122
5．22 Summary of the Averages 123
5．23 Suggestions for Further Reading 123
Exercises 123
CHAPTER Ⅵ MEASURES OF DISPERSION 126
6．1 Variability 126
6．2 The Range 127
6．3 The Semi-interquartile Range 128
6．4 The Average Deviation 130
6．5 The Standard Deviation 135
6．6 Standard Deviation：Ungrouped Data 136
6．7 Standard Deviation：Grouped Data 139
6．8 Checking Accuracy of Computations 143
6．9 Meaning of the Standard Deviation 144
6．10 Variance 147
6．11 Measurement of Relative Dispersion 149
6．12 Suggestions for Further Reading 153
Exercises 153
CHAPTER Ⅶ SIMPLE PROBABILITY AND THE NORMAL CURVE 155
7．1 Probability 155
7．2 Mean and Standard Deviation of Probability Data 157
7．3 Elementary Theorems 159
7．4 Expansion of the point Binomial 160
7．5 The Normal Curve 163
7．6 Areas under the Normal Curve 167
7．7 Preliminary Tests for Normality 172
7．8 Fitting the Normal Curve：Method of Ordinates 177
7．9 Fitting the Normal Curve：Method of Areas 181
Exercises 185
CHAPTER Ⅷ MOMENTS，FREQUENCY CURVES，AND THE CHI-SQUARE TEST 187
8．1 The Higher Moments of a Frequency Distribution 187
8．2 Computation of the Higher Moments 189
8．3 Checking Accuracy of Computations 193
8．4 Grouping Error 194
8．5 Moments of Probability Distributions 196
8．6 Measures of Skewness 200
8．7 Measures of Kurtosis 206
8．8 Interpretation of Frequency Statistics 208
8．9 ThePearsonian System of Frequency Curves 211
8．10 Fitting Pearson＇s Type Ⅲ Curve 212
8．11 The Poisson Series 215
8．12 Goodness of Fit and the Chi-square Test 221
8．13 Suggestions for Further Reading 229
Exercises 230
CHAPTER Ⅸ MEASURES OF RELIABILITY 233
9．1 Sample and Universe 233
9．2 Standard Error of the Arithmetic Mean 236
9．3 The Probable Error 242
9．4 Other Standard Errors 243
of the Standard Deviation 244
of the Median 245
of the Alphas 245
of a Relative Frequency(Percentage) 247
of the Semi-interquartile Range 248
of the Average Deviation 248
of Either Quartile 248
of β2 249
of Measures of Skewness 249
of the Coefficient of Variation 249
of the Difference between Two Measures 250
of the Sum of Two Measures 253
9．5 The Significance of Differences 253
9．6 Fiducial Probability and the Confidence Interval 258
9．7 Suggestions for Further Reading 261
Exercises 261
CHAPTER Ⅹ THE ANALYSIS OF VARIANCE 264
10．1 Combining Frequency Distributions 264
10．2 Contributions to Combined Variance 268
10．3 Purpose of Analysis of Variance 269
10．4 The Concept of Degrees of Freedom 271
10．5 Computation of Analysis of Variance 275
10．6 Summary of Steps in Analysis of Variance 284
10．7 Suggestions for Further Reading 286
Exercises 286
CHAPTER Ⅺ FITTING STRAIGHT LINES 289
11．1 The Use of Two Variables 289
11．2 The Nature of Relationship 291
11．3 Simple Methods of Finding Relationships 294
11．4 The Scatter Diagram 297
11．5 Regression Lines and Trend Lines 301
11．6 The Freehand Linear Trend 303
11．7 The Method of Selected Points 304
11．8 The Method of Least Squares 307
11．9 Fitting a Straight Line by Least Squares 311
11．10 Interpreting Results of Regression Formulas 316
11．11 The Residuals or Errors 320
11．12 Short Cuts with Historical Data 322
11．13 The Direction of Dependence 328
11．14 Elimination of Trend 333
11．15 Suggestions for Further Reading 337
Exercises 337
CHAPTER Ⅻ CURVE FITTING 340
12．1 Discovering Curvilinearity 340
12．2 Common Curve Types 342
12．3 The Second-degree Parabola 344
12．4 The Third-degree Parabola 352
12．5 The Semilogarithmic or Exponential Curve 354
12．6 The Concept of Half-life 359
12．7 The Logarithmic Curve 362
12．8 The Reciprocal Curve 366
12．9 Deciding the Type of Curve to Fit 369
12．10 Comparison with Type Curves 371
12．11 The Process of Differencing 372
12．12 Plotting＂Distorted Data．＂ 375
12．13 Plotting Data on Distorted Axes 376
12．14 Summary 380
12．15 Suggestions for Further Reading 382
Exercises 382
CHAPTER ⅩⅢ HISTORICAL DATA 386
13．1 Types of Movements in Historical Data 386
13．2 The Secular Trend 389
13．3 The Progressive Mean 392
13．4 Advantages and Disadvantages of the Moving Average 393
13．5 The Nature of Cyclical Movements 394
13．6 Comon Periods of Cycles 397
13．7 Seasonal Variation Measured Around the Moving Average 399
13．8 Seasonal Variation by Link Relatives 408
13．9 The Elimination of Seasonal Movements 411
13．10 Random Movements 413
13．11 The Concept of the Statistical Normal 416
13．12 Suggestions for Further Reading 418
Exercises 418
CHAPTER ⅩⅣ INDEX NUMBERS 420
14．1 A Simple Aggregative Index Number 421
14．2 Averages of Relatives 422
14．3 Bias in Index Numbers 423
14．4 Weighting of Index Numbers 424
14．5 Weight Bias 428
14．6 Uses of Index Numbers 429
14．7 Correcting Prices with Index Numbers 431
14．8 The Choice of a Base Period for Index Numbers 434
14．9 Link Relatives and Chain Indices 435
14．10 Choosing a Formula for Index Numbers 437
14．11 Selection of Basic Data 439
14．12 Suggestions for Further Reading 439
Exercises 440
CHAPTER ⅩⅤ SIMPLE CORRELATION 442
15．1 Errors of Estimate 442
15．2 Correlation 446
15．3 Degrees of Freedom 450
15．4 Standard Error of Correlation Coefficient 451
15．5 The z-transformation 452
15．6 Actual Computations 454
15．7 Computation of Regression Equations 457
15．8 Computing the Standard Error of Estimate 457
15．9 Illustrative Problem 458
15．10 Interpretation of Correlation Coefficients 464
15．11 Correlation of Grouped Data 474
15．12 Simple Curvilinear Correlation 481
15．13 Corrections for Degrees of Freedom 484
15．14 Linear and Curvilinear Correlation Compared 486
15．15 Standard Errors in Curvilinear Correlation 487
15．16 Suggestions for Further Reading 488
Exercises 488
CHAPTER ⅩⅥ MULTIPLE CORRELATION 493
16．1 Nature of Multiple Relationships 493
16．2 Dependent and Independent Variables 494
16．3 Multiple-regression Equations 495
16．4 Types of Relationship 498
16．5 Methods of Computation 502
16．6 Effects of Variables Separately 506
16．7 Other Correlation Constants 508
16．8 Corrections for Degrees of Freedom 509
16．9 Standard Errors of Coefficients of Multiple Correlation 509
16．10 Suggestions for Further Reading 510
Exercises 510
APPENDIXES 513
Ⅰ．Areas under the Normal Curve 514
Ⅱ．Ordinates of the Normal Curve 515
Ⅲ．1 Per Cent and 5 Per Cent Significant Points of F 516
Ⅳ．Values of r for Various Values of z from 1 to 3 520
Author Index 521
Subject Index 523