**Statistics for Textile and Apparel Management**

by J. Hayavadana

**Contents**

Foreword ix

Preface xi

**1 Introduction to statistics in textiles 1 **

1.1 Introduction 1

1.2 Salient features of statistics 3

1.3 Functions of statistics 3

1.4 Applications of statistical tools in various processing stages of textile production 4

1.5 Scope of statistical techniques in textile production 6

1.6 Limitations of statistics 9

**2 Treatment of data and construction of frequency distribution 11 **

2.1 Introduction 11

2.2 Statistical series 12

2.3 Classification and tabulation 13

2.4 Methods of collecting primary data 13

2.5 Methods of collecting secondary data 13

2.6 Classification of data 13

2.7 Tabulation 14

2.8 Problems for practice 15

2.9 Construction of frequency distribution 16

2.10 Formulae to calculate the number of CI 18

2.11 Numerical examples on construction of frequency distribution 18

**3 Measures of central tendency 26 **

3.1 Introduction 26

3.2 Objectives of averaging 26

3.3 Calculation of ‘simple’ arithmetic mean – individual 31 observations – case (i)

3.4 Calculation of mean 33

3.5 Mathematical property of median 41

3.6 Different types of mean and their importance 42

3.7 Properties of arithmetic mean 45

3.8 Weighted geometric mean 53

3.9 Harmonic mean 56

3.10 Problems on missing frequency 57

3.11 Median 58

3.12 Mode 65

3.13 Measures of variability 69

3.14 Deviation score method 73

3.15 Short-Cut method (Assumed mean method) 76

3.16 Mathematical properties of standard deviation 80

3.17 Correcting incorrect values of mean and standard deviation 81

3.18 Problems on co-efficient of variation 84

3.19 Calculation of standard deviation – discrete, individual 87

3.20 Problems on “missing information” in properties of SD 91

3.21 “Inter-quartile range” problems, special problems on “SD”, coefficient of SD 92

3.22 Problems on “CI” determination from “SD”, “mean”, Deviation and ‘f’ 95

3.23 Harmonic mean 96

Problem for practice 97

**4 Measures of dispersion 98 **

4.1 Introduction 98

4.2 The measure of the variation of the items 98

4.3 Significance of measuring dispersion/variation 99

4.4 Range and its importance 101

4.5 Quartile deviation 102

**5 Theoretical distributions 104 **

5.1 Normal distribution 104

5.2 Patterns of variation 123

5.3 Tchebycheff’s inequality 128

5.4 Normal approximation to binomial distribution 131

5.5 The binomial distribution 134

5.6 The central limit theorem 140

5.7 Significance test for the difference between two rates of occurrence 142

5.8 Confidence interval for mean rate of occurrence 143

**6 Correlation 148 **

6.1 Partial and multiple correlations 157

6.2 Partial correlation 158

6.3 How to find partial correlation coefficients 158

6.4 Method to calculate multiple correlation coefficients 162

6.5 Regression equations and regression coefficients 167

**7 Linear regression 170 **

7.1 Introduction 170

7.2 Regression equations and coefficients 170

7.3 Standard error of estimate 178

7.4 Ratio of variation 179

7.5 Galton graph and regression line 180

7.6 How to find the ratio of regression 183

7.7 Variation about the regression line and its significance 187

7.8 Confidence limits 188

7.9 Tests for regression 189

**8 Time series 193 **

8.1 Introduction 193

8.2 Utility of time series 194

8.3 Components of time series 194

8.4 Measurement of trend 197

8.5 Methods of least square 198

8.6 Linear trend 198

8.7 Quadratic trend (parabolic trend) 202

8.8 Exponentional trend 205

8.9 Methods of semi-averages 209

8.10 Method of moving averages 211

**9 Control charts 213**

9.1 Introduction 213

9.2 Basis of control limits 213

9.3 Causes of variation in quality 214

9.4 Nature of a control chart 215

9.5 Interpretation of control charts 217

9.6 First construct of⎯R chart 229

9.7 Type I and Type II errors 232

9.8 The ó chart 233

9.9 Charts for attributes 235

9.10 Determining the control limits 245

**10 Tests of significance 253 **

10.1 Introduction 253

10.2 Z-Test of significance of coefficient of correlation 260

10.3 Test of significance of difference between two coefficients of correlation 261

10.4 Testing difference between means of two samples 275

10.5 Testing the significance of an observed correlation coefficient 277

10.6 Test of goodness of fit 287

11 Analysis of variance 290

11.1 Introduction 290

11.2 Variance ratio 292

11.3 Calculation of variance ratio or F 293

11.4 Interpretation of F 294

11.5 Other designs – three-way classification – latin square 334

Appendices 347

Index 354

**Preface **

I am pleased to release my first book titled “Statistics for Textiles and Apparel Management” to my textile fraternity. Indeed it is a common experience of a student to feel shortage of textile books as compared to other fields and it is a fact also. Statistics is such an important subject without which the business world would have perished. Any product development or production without quality control is like a lifeless object. Textile production is not an exception and any research concludes its results using statistical techniques.

It was my long cherished dream to write a book on statistical methods for textile production and it took nearly 6 years to finalise the topics and book.

The book primarily caters the need to learn basics of statistics in textile production. The book is organized in 11 chapters with examples at each point of discussion. I hope that book will leave up to the expectations of textile world. Any help in the form of suggestions or guidelines, etc., in improving the quality of the book is highly appreciable and will be suitably acknowledged.

J. Hayavadana