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| a concise course in a level statistics: A Concise Course in Advanced Level Statistics Janet Crawshaw, Joan Chambers, 2001 New in this edition is a 20 page section on the use of ICT resources in teaching and learning about statistics. The book also includes over 300 worked examples and advice on how to break down calculations into easy stages. |
| a concise course in a level statistics: A Concise Course in A-level Statistics J. Crawshaw, Joan Chambers, 1994 Written to cover the Statistics elements of an A-Level Mathematics course, this book has been updated to cover all Boards' syllabus requirements for first examination in 1996. It presents theory, supported throughout by worked examples, and further consolidation in the form of graded exercises. |
| a concise course in a level statistics: All of Statistics Larry Wasserman, 2004-09-17 This book is for people who want to learn probability and statistics quickly. It brings together many of the main ideas in modern statistics in one place. The book is suitable for students and researchers in statistics, computer science, data mining and machine learning. This book covers a much wider range of topics than a typical introductory text on mathematical statistics. It includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses. The reader is assumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. The text can be used at the advanced undergraduate and graduate level. Larry Wasserman is Professor of Statistics at Carnegie Mellon University. He is also a member of the Center for Automated Learning and Discovery in the School of Computer Science. His research areas include nonparametric inference, asymptotic theory, causality, and applications to astrophysics, bioinformatics, and genetics. He is the 1999 winner of the Committee of Presidents of Statistical Societies Presidents' Award and the 2002 winner of the Centre de recherches mathematiques de Montreal–Statistical Society of Canada Prize in Statistics. He is Associate Editor of The Journal of the American Statistical Association and The Annals of Statistics. He is a fellow of the American Statistical Association and of the Institute of Mathematical Statistics. |
| a concise course in a level statistics: A Concise Course in A-Level Statistics with Worked Examples J. Crawshaw, Joan Chambers, 1987-01-01 |
| a concise course in a level statistics: Theoretical Statistics Robert W. Keener, 2010-09-08 Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis. The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix. |
| a concise course in a level statistics: A concise course in A-level statistics J. Crawshaw, J. Chambers, 1984 |
| a concise course in a level statistics: Theory of Spatial Statistics M.N.M. van Lieshout, 2019-03-19 Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics. |
| a concise course in a level statistics: Beginning Statistics with Data Analysis Frederick Mosteller, Stephen E. Fienberg, Robert E.K. Rourke, 2013-11-20 This introduction to the world of statistics covers exploratory data analysis, methods for collecting data, formal statistical inference, and techniques of regression and analysis of variance. 1983 edition. |
| a concise course in a level statistics: Core Statistics Simon N. Wood, 2015-04-13 Core Statistics is a compact starter course on the theory, models, and computational tools needed to make informed use of powerful statistical methods. |
| a concise course in a level statistics: OpenIntro Statistics David Diez, Christopher Barr, Mine Çetinkaya-Rundel, 2015-07-02 The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources. |
| a concise course in a level statistics: Statistical Theory Felix Abramovich, Ya'acov Ritov, 2013-04-25 Designed for a one-semester advanced undergraduate or graduate course, Statistical Theory: A Concise Introduction clearly explains the underlying ideas and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, and elements of decision theory. It i |
| a concise course in a level statistics: A First Course In Probability And Statistics B L S Prakasa Rao, 2008-12-22 Explanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software explain how to conduct data analysis, but do not explain when to apply and when not to apply it. Keeping this in view, we try to explain the basic concepts of probability and statistics for students with an understanding of a first course in calculus at the undergraduate level.Designed as a textbook for undergraduate and first-year graduate students in statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering sciences and computer science programs, it provides a clear exposition of the theory of probability along with applications in statistics. The book contains a large number of solved examples and chapter-end exercises designed to reinforce the probability theory and emphasize statistical applications. |
| a concise course in a level statistics: Introductory Statistics 2e Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| a concise course in a level statistics: Online Statistics Education David M Lane, 2014-12-02 Online Statistics: An Interactive Multimedia Course of Study is a resource for learning and teaching introductory statistics. It contains material presented in textbook format and as video presentations. This resource features interactive demonstrations and simulations, case studies, and an analysis lab.This print edition of the public domain textbook gives the student an opportunity to own a physical copy to help enhance their educational experience. This part I features the book Front Matter, Chapters 1-10, and the full Glossary. Chapters Include:: I. Introduction, II. Graphing Distributions, III. Summarizing Distributions, IV. Describing Bivariate Data, V. Probability, VI. Research Design, VII. Normal Distributions, VIII. Advanced Graphs, IX. Sampling Distributions, and X. Estimation. Online Statistics Education: A Multimedia Course of Study (http: //onlinestatbook.com/). Project Leader: David M. Lane, Rice University. |
| a concise course in a level statistics: Statistics of Financial Markets Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner, 2008-01-08 Readers will find that, refreshingly, this text presents in a vivid yet concise style the necessary statistical and mathematical background for financial engineers. The focus is both on fundamentals of mathematical finance and financial time series analysis and on applications to given problems of financial markets, making the book the ideal basis for lectures, seminars and crash courses on the topic. For the second edition the book has been updated and extensively revised. Several new topics have been included, such as a chapter on credit risk management. |
| a concise course in a level statistics: The Statistical Analysis of Experimental Data John Mandel, 2012-06-08 First half of book presents fundamental mathematical definitions, concepts, and facts while remaining half deals with statistics primarily as an interpretive tool. Well-written text, numerous worked examples with step-by-step presentation. Includes 116 tables. |
| a concise course in a level statistics: Introductory Business Statistics 2e Alexander Holmes, Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| a concise course in a level statistics: A Concise Course in A-level Statistics J. Crawshaw, J. Chambers, 1983 |
| a concise course in a level statistics: Applying and Interpreting Statistics Glen McPherson, 2001-04-27 Of interest to graduate students and researchers in many areas, this book explains the use of statistics in scientific investigations. It describes the basis, application, and interpretation of statistics and the wide range of statistical methodologies. |
| a concise course in a level statistics: Statistical Analysis and Data Display Richard M. Heiberger, Burt Holland, 2013-06-29 1 Audience Students seeking master's degrees in applied statistics in the late 1960s and 1970s typically took a year-long sequence in statistical methods. Popular choices of the course text book in that period prior to the availability of high speed computing and graphics capability were those authored by Snedecor and Cochran, and Steel and Torrie. By 1980, the topical coverage in these classics failed to include a great many new and important elementary techniques in the data analyst's toolkit. In order to teach the statistical methods sequence with adequate coverage of topics, it became necessary to draw material from each of four or five text sources. Obviously, such a situation makes life difficult for both students and instructors. In addition, statistics students need to become proficient with at least one high-quality statistical software package. This book can serve as a standalone text for a contemporary year-long course in statistical methods at a level appropriate for statistics majors at the master's level or other quantitatively oriented disciplines at the doctoral level. The topics include both concepts and techniques developed many years ago and a variety of newer tools not commonly found in textbooks. |
| a concise course in a level statistics: Collaborative Statistics Barbara Illowsky, Susan Dean, 2015-02-18 Collaborative Stastistics is intended for introductory statistics courses being taken by students at two- and four-year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. Barbara Illowsky and Susan Dean are professors of mathematics and statistics at De Anza College in Cupertino, CA. They present nationally on integrating technology, distance learning, collaborative learning, and multiculturalism into the elementary statistics classroom. |
| a concise course in a level statistics: Statistics 4 Greg Attwood, Gill Dyer, Gordon Skipworth, 2001 A syllabus-specific textbook providing worked examples, exam-level questions and many practice exercises, in accordance to the new Edexcel AS and Advanced GCE specification. |
| a concise course in a level statistics: Introduction to Probability Charles Miller Grinstead, James Laurie Snell, 2012-10-30 This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. |
| a concise course in a level statistics: Think Stats Allen B. Downey, 2011-07-01 If you know how to program, you have the skills to turn data into knowledge using the tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and concepts. Develop your understanding of probability and statistics by writing and testing code Run experiments to test statistical behavior, such as generating samples from several distributions Use simulations to understand concepts that are hard to grasp mathematically Learn topics not usually covered in an introductory course, such as Bayesian estimation Import data from almost any source using Python, rather than be limited to data that has been cleaned and formatted for statistics tools Use statistical inference to answer questions about real-world data |
| a concise course in a level statistics: Essentials of Statistics Mario F. Triola, 2015 From SAT scores to job search methods, statistics influences and shapes the world around us. Marty Triola's text continues to be the bestseller because it helps students understand the relationship between statistics and the world, bringing life to the theory and methods. Essentials of Statistics (a briefer version of Elementary Statistics-see below for the full series) raises the bar with every edition by incorporating an unprecedented amount of real and interesting data that will help instructors connect with students today, and help them connect statistics to their daily lives. The Fifth Edition contains more than 1,585 exercises, 89% of which use real data and 86% of which are new. |
| a concise course in a level statistics: Understanding Statistics Graham Upton, Ian Cook, 1996 Covers topics in statistics required for A-Level Mathematics. |
| a concise course in a level statistics: A Modern Introduction to Probability and Statistics F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester, 2006-03-30 Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to modern methods such as the bootstrap. |
| a concise course in a level statistics: Modern Mathematical Statistics with Applications Jay L. Devore, Kenneth N. Berk, 2011-12-07 Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data. The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research. It begins with a chapter on descriptive statistics that immediately exposes the reader to real data. The next six chapters develop the probability material that bridges the gap between descriptive and inferential statistics. Point estimation, inferences based on statistical intervals, and hypothesis testing are then introduced in the next three chapters. The remainder of the book explores the use of this methodology in a variety of more complex settings. This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics. Representative applications include investigating whether the average tip percentage in a particular restaurant exceeds the standard 15%, considering whether the flavor and aroma of Champagne are affected by bottle temperature or type of pour, modeling the relationship between college graduation rate and average SAT score, and assessing the likelihood of O-ring failure in space shuttle launches as related to launch temperature. |
| a concise course in a level statistics: Using Statistics in Social Research Scott M. Lynch, 2013-09-07 This book covers applied statistics for the social sciences with upper-level undergraduate students in mind. The chapters are based on lecture notes from an introductory statistics course the author has taught for a number of years. The book integrates statistics into the research process, with early chapters covering basic philosophical issues underpinning the process of scientific research. These include the concepts of deductive reasoning and the falsifiability of hypotheses, the development of a research question and hypotheses, and the process of data collection and measurement. Probability theory is then covered extensively with a focus on its role in laying the foundation for statistical reasoning and inference. After illustrating the Central Limit Theorem, later chapters address the key, basic statistical methods used in social science research, including various z and t tests and confidence intervals, nonparametric chi square tests, one-way analysis of variance, correlation, simple regression, and multiple regression, with a discussion of the key issues involved in thinking about causal processes. Concepts and topics are illustrated using both real and simulated data. The penultimate chapter presents rules and suggestions for the successful presentation of statistics in tabular and graphic formats, and the final chapter offers suggestions for subsequent reading and study. |
| a concise course in a level statistics: Mathematical Statistics with Applications in R Kandethody M. Ramachandran, Chris P. Tsokos, 2018-11-13 Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner. This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students. Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods |
| a concise course in a level statistics: Advanced High School Statistics David Diez, Christopher Barr, Mine Çetinkaya-Rundel, Leah Dorazio, 2014-07-30 A free PDF copy of this textbook may be found on the project's website (do an online search for OpenIntro). This is a Preliminary Edition of a new textbook by OpenIntro that is focused on the advanced high school level.Chapters: 1 - Data Collection,2 - Summarizing Data,3 - Probability,4 - Distributions of Random Variables,5 - Foundation for Inference,6 - Inference for Categorical Data,7 - Inference for Numerical Data,8 - Introduction to Linear Regression. |
| a concise course in a level statistics: Probability and Statistics Michael J. Evans, Jeffrey S. Rosenthal, 2010-03-01 Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor to the course, incorporating the computer and offering an integrated approach to inference that includes the frequency approach and the Bayesian inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout. Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. The new edition includes a number of features designed to make the material more accessible and level-appropriate to the students taking this course today. |
| a concise course in a level statistics: A Level Mathematics for Edexcel: Statistics S1 James Nicholson, 2008-02-14 Oxford A Level Mathematics for Edexcel takes a completely fresh look at presenting the challenges of A Level. It specifically targets average students, with tactics designed to offer real chance of success to more students, as well as providing more stretch and challenge material. This Statistics 1 book includes a background knowledge chapter to help bridge the gap between GCSE and A level study. |
| a concise course in a level statistics: Mathematical Statistics and Data Analysis John A. Rice, 2007 This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings. |
| a concise course in a level statistics: Introductory Statistics Douglas S. Shafer, 2022 |
| a concise course in a level statistics: Business Mathematics and Statistics Andy Francis, 2000 |
| a concise course in a level statistics: Book of R Tilman Davies M., 2016 |
| a concise course in a level statistics: Schaum's Outline of Theory and Problems of Probability and Statistics Murray R. Spiegel, 1996 |
| a concise course in a level statistics: Lies, Damned Lies, Or Statistics Jonathan Poritz, 2017-05-13 An intro to statistics. |
CONCISE Definition & Meaning - Merriam-Webster
The meaning of CONCISE is marked by brevity of expression or statement : free from all elaboration and superfluous detail. How to use concise in a sentence. Did you know?
CONCISE | English meaning - Cambridge Dictionary
CONCISE definition: 1. short and clear, expressing what needs to be said without unnecessary words: 2. short and…. Learn more.
CONCISE Definition & Meaning | Dictionary.com
Concise definition: expressing or covering much in few words; brief in form but comprehensive in scope; succinct; terse.. See examples of CONCISE used in a sentence.
CONCISE definition and meaning | Collins English Dictionary
Jun 9, 2016 · Something that is concise says everything that is necessary without using any unnecessary words. Burton's text is concise and informative. Whatever you are writing make sure …
Concise - Definition, Meaning & Synonyms | Vocabulary.com
If something is concise, it's short and gets right to the point. A concise edition of your diary might be 50 pages of the most important entries. Concise comes from the Latin word concidere, which …
Concise - definition of concise by The Free Dictionary
concise implies that unnecessary details or verbiage have been eliminated: a concise summary of a speech. succinct suggests clarity of expression as well as brevity: praised for her succinct …
concise adjective - Definition, pictures, pronunciation and usage …
Definition of concise adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
CONCISE Synonyms: 58 Similar and Opposite Words - Merriam-Webster
Some common synonyms of concise are compendious, laconic, pithy, succinct, summary, and terse. While all these words mean "very brief in statement or expression," concise suggests the …
concise - WordReference.com Dictionary of English
Concise, succinct, terse all refer to speech or writing that uses few words to say much. Concise usually implies that unnecessary details or verbiage have been eliminated from a more wordy …
Concise Definition & Meaning | Britannica Dictionary
concise, terse, succinct, laconic, and pithy mean expressing or stating an idea by using only a few words. concise is the most general of these words and suggests a lack of extra or unnecessary …
CONCISE Definition & Meaning - Merriam-Webster
The meaning of CONCISE is marked by brevity of expression or statement : free from all elaboration and superfluous detail. How to use concise in a sentence. Did you know?
CONCISE | English meaning - Cambridge Dictionary
CONCISE definition: 1. short and clear, expressing what needs to be said without unnecessary words: 2. short and…. Learn more.
CONCISE Definition & Meaning | Dictionary.com
Concise definition: expressing or covering much in few words; brief in form but comprehensive in scope; succinct; terse.. See examples of CONCISE used in a sentence.
CONCISE definition and meaning | Collins English Dictionary
Jun 9, 2016 · Something that is concise says everything that is necessary without using any unnecessary words. Burton's text is concise and informative. Whatever you are writing make …
Concise - Definition, Meaning & Synonyms | Vocabulary.com
If something is concise, it's short and gets right to the point. A concise edition of your diary might be 50 pages of the most important entries. Concise comes from the Latin word concidere, …
Concise - definition of concise by The Free Dictionary
concise implies that unnecessary details or verbiage have been eliminated: a concise summary of a speech. succinct suggests clarity of expression as well as brevity: praised for her succinct …
concise adjective - Definition, pictures, pronunciation and usage …
Definition of concise adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
CONCISE Synonyms: 58 Similar and Opposite Words - Merriam-Webster
Some common synonyms of concise are compendious, laconic, pithy, succinct, summary, and terse. While all these words mean "very brief in statement or expression," concise suggests …
concise - WordReference.com Dictionary of English
Concise, succinct, terse all refer to speech or writing that uses few words to say much. Concise usually implies that unnecessary details or verbiage have been eliminated from a more wordy …
Concise Definition & Meaning | Britannica Dictionary
concise, terse, succinct, laconic, and pithy mean expressing or stating an idea by using only a few words. concise is the most general of these words and suggests a lack of extra or …
