**Statistics for Textile Engineers**

by J. R. Nagla

**Contents**

1 Introduction and need of statistics 1

1.1 Introduction 1

1.2 Nature of textile industry today 1

1.3 Need for SQC techniques 2

2 Statistics and basic concepts 5

2.1 Introduction of statistics 5

2.2 Methods of data collection 7

3 Classification and graphical representations 9

3.1 Introduction 9

3.2 Frequency distribution table 10

3.3 Cumulative frequency distribution table 16

3.4 Graphical representations of the frequency distribution 18

3.5 Graphical representations of the cumulative frequency distribution (Ogive Curve) 20

3.6 Exercise 22

4 Measures of central tendency 25

4.1 Introduction of the central tendency 25

4.2 Measure of central tendency 25

4.3 Arithmetic mean 25

4.4 Computation of AM for the frequency distribution 26

4.5 Median 31

4.6 Computation of median 31

4.7 Graphical determination of median 32

4.8 Mode 35

4.9 Determination of mode 35

4.10 Determination of mode graphically 36

4.11 Exercise 38

5 Partition values 40

5.1 Introduction 40

5.2 Quartiles 40

5.3 Deciles 45

5.4 Percentiles 50

5.5 Exercise 54

6 Measures of dispersion 56

6.1 Introduction of the dispersion 56

6.2 Range 56

6.3 Quartile deviation 58

6.4 Mean deviation 61

6.5 Standard deviation 65

6.6 Relative measures of dispersion 72

6.7 Exercise 76

7 Skewness and kurtosis 80

7.1 Introduction 80

7.2 Skewness 80

7.3 Symmetric frequency distribution 80

7.4 Skewed frequency distribution 81

7.5 Measures of skewness 82

7.6 Interpretation of the coefficient of skewness 83

7.7 Kurtosis 85

7.8 Measures of kurtosis 86

7.9 Exercise 88

8 Correlation and regression 90

8.1 Introduction 90

8.2 Bivariate data 90

8.3 Correlation analysis 90

8.4 Coefficient of determination 93

8.5 Spearman’s rank correlation coefficient 95

8.6 Regression analysis 100

8.7 Exercise 108

9 Multivariate analysis 111

9.1 Introduction 111

9.2 Multivariate data 111

9.3 Multiple correlation analysis 111

9.4 Multiple regression analysis 114

9.5 Exercise 117

10 Probability 119

10.1 Introduction 119

10.2 Basic concepts 119

10.3 Definition of the probability (classical approach) 122

10.4 Laws of the probability 122

10.5 Results of permutation and combination 123

10.6 Exercise 129

11 Probability distributions 131

11.1 Basic concepts 131

11.2 Probability distribution of a random variable 132

11.3 Some properties of the random variable and its probability distribution 136

11.4 Some standard probability distributions 138

11.5 Exercise 138

12 Standard discrete probability distributions 140

12.1 Binomial probability distribution 140

12.2. Poisson probability distribution 143

12.3 Poisson approximation to the binomial distribution 146

12.4 Fitting of binomial and Poisson probability distributions 147

12.5 Exercise 151

13 Standard continuous probability distributions 154

13.1 Normal problem distribution 154

13.2 Standard normal variable and standard normal probability distribution 157

13.3 Chi-square probability distribution (χ2 distribution) 162

13.4 Student’s t-probability distribution 164

13.5 F-probability distribution 166

13.6 Exercise 168

14 Testing of hypothesis 170

14.1 Introduction 170

14.2 Large sample tests (Z-tests) 172

14.3 Small sample tests 185

14.4 Exercise 216

15 Estimation 220

15.1 Introduction 220

15.2 Point estimation 220

15.3 Interval estimation (confidence interval) 222

15.4 Exercise 229

16 Analysis of variance 231

16.1 Introduction 231

16.2 One-way analysis of variance 232

16.3 Two-way analysis of variance 238

16.4 Exercise 249

17 Design of experiments 253

17.1 Introduction 253

17.2. Completely randomized design 254

17.3. Randomized block design 255

17.4. Latin square design (LSD) 257

17.5 Factorial experiments 262

17.6 Exercise 274

18 Statistical quality control 278

18.1 Introduction 278

18.2 Process control 279

18.3 Control chart 279

18.4 Interpretation of control chart 280

18.5 Specification limits 281

18.6 X chart 281

18.7 R-Chart 282

18.8 np-Chart 284

18.9 p-Chart 285

18.10 C-chart 288

18.11 Lot control 290

18.12 Some basic concepts related to rectifying single sampling plan 291

18.13 Exercise 294

Area under standard normal curve from Z = 0 to Z = z 296

tn,∝/2values for t-distribution 298

χ2n,∝ values for χ2-distribution 300

Fm,n, 0.05 values for F-distribution 302

Fm,n, 0.01 values for F-distribution 304

Statistical constants for control charts 306

Index 308

**Preface**

The inspiration of writing this book is the result of great need from textile engineering students, textile engineers and textile professionals working in the textile industries for the book on statistics in simple and easy language, which will guide and help them to use different statistical methods in decision making.

I hope this book will meet all the needs of textile professionals and textile industries in their decision making as it discusses everything related to statistics right from basic data collection to up to design of experiments with suitable illustrations. Though this book is written for textile-related people only, it is also useful for engineers or researchers of any discipline. The statistical tables of the book are created using Microsoft Excel functions.

I am thankful to Shri. K. Venkatrayan (BITRA Mumbai) for his guidance in writing this book. I am very much thankful to Professor S. D. Mahajan (TEI Ichalkaranji) for writing the introductory chapter, also editing and proof reading the book. I am thankful to my student Raghav Bhala for his help in checking calculations. I am very much thankful to our principal

Dr. P. V. Kadole and the management of DKTE Society for their support and help in completing this book. Finally, I am thankful to those who have inspired and helped me directly or indirectly in writing this book. I will be happy if the readers point out mistakes and give feedback about the book.

J. R. Nagla

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