CHAPTER Ⅰ THE NATURE OF STATISTICS

1．1 Scientific Method

1．2 Experimental Method

1．3 Statistical Method

1．4 Statistics

1．5 Preliminary Admonitions

1．6 Suggestions for Further Reading

CHAPTER Ⅱ THE MEANING OF NUMBERS

2．1 Accuracy of Measurement

2．2 Biassed and Compensating Errors

2．3 Significant Figures

2．4 Standard Notation

2．5 Computations with Approximate Nubmers

2．6 Multiplication and Division of Approximate Numbers

2．7 Addition and Subtraction of Approximate Numbers

2．8 A Horrible Example

2．9 Rounding Off Numbers

2．10 Suggestions for Further Reading

Exercises

CHAPTER Ⅲ THE FREQUENCY DISTRIBUTION

3．1 The Frequency Table

3．2 Class Limits

3．3 Overlapping Class Limits

3．4 Open-end Classes

3．5 Class Intervals

3．6 Class Marks

3．7 Cumulative Frequency Tables

3．8 Graphic Presentation：the Histogram

3．9 Graphic Presentation：the Frequency Polygon

3．10 Graphic Presentation：the Frequency Curve

3．11 Graphic Presentation：the Ogive

3．12 What to Look for in a Frequency Table

3．13 Common Shapes of Frequency Curves

3．14 Common Shapes of Ogives

3．15 Making a Frequency Table：How Many Classes？

3．16 Making a Frequency Table：Rules of Thumb

3．17 Making a Frequency Table：Choosing the Class Interval

3．18 When to Use Unequal Class Intervals

3．19 How to Use Unequal Class Intervals

3．20 Logarithmic Frequency Classes

3．21 Making a Frequency Table：Locating the Class Marks

3．22 Summary：Directions for Making a Frequency Table

3．23 Suggestions for Further Reading

Exercises

CHAPTER Ⅳ MEASURES OF CENTRAL TENDENCY

4．1 Averages

4．2 The Arithmetic Mean：Ungrouped Data

4．3 Weighted Arithmetic Mean

4．4 The Median：Ungrouped Data

4．5 The Mode：Ungrouped Data

4．6 The Geometric Mean：Ungrouped Data

4．7 The Harmonic Mean：Ungrouped Data

4．8 The Quadratic Mean：Ungrouped Data

4．9 Quartiles，Deciles，and Percentiles：Ungrouped Data

4．10 Use of Quartiles，Deciles，Etc

4．11 Summary of Averages with Ungrouped Data

Exercises

CHAPTER Ⅴ MEASURES OF CENTRAL TENDENCY(CONTINUED)

5．1 Averages from Grouped Data

5．2 The Arithmetic Mean：Grouped Data

5．3 Arithmetic Mean：Short Method

5．4 Checking Accuracy of Computations

5．5 Grouping Error with the Arithmetic Mean

5．6 The Median：Grouped Data

5．7 Finding the Median from an Ogive

5．8 The Mode：Grouped Data

5．9 The Geometric Mean：Grouped Data

5．10 The Harmonic Mean：Grouped Data

5．11 The Quadratic Mean：Grouped Data

5．12 Quartiles，Deciles，and Percentiles：Grouped Data

5．13 Summary of Averages with Grouped Data

5．14 Characteristics of a Good Average

5．15 Relationships between the Averages

5．16 Advantages and Disadvantages of the Arithmetic Mean

5．17 Advantages and Disadvantages of the Median

5．18 Advantages and Disadvantages of the Mode

5．19 Advantages and Disadvantages of the Geometric Mean

5．20 Advantages and Disadvantages of the Harmonic Mean

5．21 Advantages and Disadvantages of the Quadratic Mean

5．22 Summary of the Averages

5．23 Suggestions for Further Reading

Exercises

CHAPTER Ⅵ MEASURES OF DISPERSION

6．1 Variability

6．2 The Range

6．3 The Semi-interquartile Range

6．4 The Average Deviation

6．5 The Standard Deviation

6．6 Standard Deviation：Ungrouped Data

6．7 Standard Deviation：Grouped Data

6．8 Checking Accuracy of Computations

6．9 Meaning of the Standard Deviation

6．10 Variance

6．11 Measurement of Relative Dispersion

6．12 Suggestions for Further Reading

Exercises

CHAPTER Ⅶ SIMPLE PROBABILITY AND THE NORMAL CURVE

7．1 Probability

7．2 Mean and Standard Deviation of Probability Data

7．3 Elementary Theorems

7．4 Expansion of the point Binomial

7．5 The Normal Curve

7．6 Areas under the Normal Curve

7．7 Preliminary Tests for Normality

7．8 Fitting the Normal Curve：Method of Ordinates

7．9 Fitting the Normal Curve：Method of Areas

Exercises

CHAPTER Ⅷ MOMENTS，FREQUENCY CURVES，AND THE CHI-SQUARE TEST

8．1 The Higher Moments of a Frequency Distribution

8．2 Computation of the Higher Moments

8．3 Checking Accuracy of Computations

8．4 Grouping Error

8．5 Moments of Probability Distributions

8．6 Measures of Skewness

8．7 Measures of Kurtosis

8．8 Interpretation of Frequency Statistics

8．9 ThePearsonian System of Frequency Curves

8．10 Fitting Pearson＇s Type Ⅲ Curve

8．11 The Poisson Series

8．12 Goodness of Fit and the Chi-square Test

8．13 Suggestions for Further Reading

Exercises

CHAPTER Ⅸ MEASURES OF RELIABILITY

9．1 Sample and Universe

9．2 Standard Error of the Arithmetic Mean

9．3 The Probable Error

9．4 Other Standard Errors

of the Standard Deviation

of the Median

of the Alphas

of a Relative Frequency(Percentage)

of the Semi-interquartile Range

of the Average Deviation

of Either Quartile

of β2

of Measures of Skewness

of the Coefficient of Variation

of the Difference between Two Measures

of the Sum of Two Measures

9．5 The Significance of Differences

9．6 Fiducial Probability and the Confidence Interval

9．7 Suggestions for Further Reading

Exercises

CHAPTER Ⅹ THE ANALYSIS OF VARIANCE

10．1 Combining Frequency Distributions

10．2 Contributions to Combined Variance

10．3 Purpose of Analysis of Variance

10．4 The Concept of Degrees of Freedom

10．5 Computation of Analysis of Variance

10．6 Summary of Steps in Analysis of Variance

10．7 Suggestions for Further Reading

Exercises

CHAPTER Ⅺ FITTING STRAIGHT LINES

11．1 The Use of Two Variables

11．2 The Nature of Relationship

11．3 Simple Methods of Finding Relationships

11．4 The Scatter Diagram

11．5 Regression Lines and Trend Lines

11．6 The Freehand Linear Trend

11．7 The Method of Selected Points

11．8 The Method of Least Squares

11．9 Fitting a Straight Line by Least Squares

11．10 Interpreting Results of Regression Formulas

11．11 The Residuals or Errors

11．12 Short Cuts with Historical Data

11．13 The Direction of Dependence

11．14 Elimination of Trend

11．15 Suggestions for Further Reading

Exercises

CHAPTER Ⅻ CURVE FITTING

12．1 Discovering Curvilinearity

12．2 Common Curve Types

12．3 The Second-degree Parabola

12．4 The Third-degree Parabola

12．5 The Semilogarithmic or Exponential Curve

12．6 The Concept of Half-life

12．7 The Logarithmic Curve

12．8 The Reciprocal Curve

12．9 Deciding the Type of Curve to Fit

12．10 Comparison with Type Curves

12．11 The Process of Differencing

12．12 Plotting＂Distorted Data．＂

12．13 Plotting Data on Distorted Axes

12．14 Summary

12．15 Suggestions for Further Reading

Exercises

CHAPTER ⅩⅢ HISTORICAL DATA

13．1 Types of Movements in Historical Data

13．2 The Secular Trend

13．3 The Progressive Mean

13．4 Advantages and Disadvantages of the Moving Average

13．5 The Nature of Cyclical Movements

13．6 Comon Periods of Cycles

13．7 Seasonal Variation Measured Around the Moving Average

13．8 Seasonal Variation by Link Relatives

13．9 The Elimination of Seasonal Movements

13．10 Random Movements

13．11 The Concept of the Statistical Normal

13．12 Suggestions for Further Reading

Exercises

CHAPTER ⅩⅣ INDEX NUMBERS

14．1 A Simple Aggregative Index Number

14．2 Averages of Relatives

14．3 Bias in Index Numbers

14．4 Weighting of Index Numbers

14．5 Weight Bias

14．6 Uses of Index Numbers

14．7 Correcting Prices with Index Numbers

14．8 The Choice of a Base Period for Index Numbers

14．9 Link Relatives and Chain Indices

14．10 Choosing a Formula for Index Numbers

14．11 Selection of Basic Data

14．12 Suggestions for Further Reading

Exercises

CHAPTER ⅩⅤ SIMPLE CORRELATION

15．1 Errors of Estimate

15．2 Correlation

15．3 Degrees of Freedom

15．4 Standard Error of Correlation Coefficient

15．5 The z-transformation

15．6 Actual Computations

15．7 Computation of Regression Equations

15．8 Computing the Standard Error of Estimate

15．9 Illustrative Problem

15．10 Interpretation of Correlation Coefficients

15．11 Correlation of Grouped Data

15．12 Simple Curvilinear Correlation

15．13 Corrections for Degrees of Freedom

15．14 Linear and Curvilinear Correlation Compared

15．15 Standard Errors in Curvilinear Correlation

15．16 Suggestions for Further Reading

Exercises

CHAPTER ⅩⅥ MULTIPLE CORRELATION

16．1 Nature of Multiple Relationships

16．2 Dependent and Independent Variables

16．3 Multiple-regression Equations

16．4 Types of Relationship

16．5 Methods of Computation

16．6 Effects of Variables Separately

16．7 Other Correlation Constants

16．8 Corrections for Degrees of Freedom

16．9 Standard Errors of Coefficients of Multiple Correlation

16．10 Suggestions for Further Reading

Exercises

APPENDIXES

Ⅰ．Areas under the Normal Curve

Ⅱ．Ordinates of the Normal Curve

Ⅲ．1 Per Cent and 5 Per Cent Significant Points of F

Ⅳ．Values of r for Various Values of z from 1 to 3

Author Index

Subject Index