Statistics for textile engineers

329 Pages·2014·5.049 MB·English

by  J. R. Nagla

Statistics for Textile Engineers
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Statistics
for Textile Engineers
Prof. J. R. Nagla
WOODHEAD PUBLISHING INDIA PVT LTD
New Delhi • Cambridge • Oxford • Philadelphia
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Published by Woodhead Publishing India Pvt. Ltd.
Woodhead Publishing India Pvt. Ltd., 303, Vardaan House, 7/28, Ansari Road,
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Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge,
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Woodhead Publishing USA 1518 Walnut Street, Suite1100, Philadelphia
www.woodheadpublishing.com
First published 2014, Woodhead Publishing India Pvt. Ltd.
© Woodhead Publishing India Pvt. Ltd., 2014
This book contains information obtained from authentic and highly regarded
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Woodhead Publishing India Pvt. Ltd. ISBN: 978-93-80308-37-1
Woodhead Publishing Ltd. ISBN: 978-1-78242-067-5
Woodhead Publishing Ltd. e-ISBN: 978-1-78242-071-2
Prepress by DSM Soft, Chennai
Printed and bound by Thomson Press Pvt. Ltd.
Dedicated to
DKTE and My Family
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Contents
Preface xiii
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
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viii Contents
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
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Contents ix
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
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x Contents
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
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