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Lecturer(s)
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Pata Vladimír, prof. Dr. Ing.
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Course content
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1. Basic types of statistical data. 2. Measures of central tendency for the basic and sample data set, properties, representation, use. 3. Measures of dispersion for the basic and sample data set, properties, representation, use. 4. Confidence intervals, their use in practice. 5. Statistical tolerance intervals and their use in practice. 6. Normal, normalized normal and lognormal probability distributions and their use in metrology. 7. Student's distribution and chi-square distribution, use in practice. 8. Skewness and kurtosis of measured data, central limit theorem, use in practice. 9. Law of large numbers, principle of hypothesis theory for continuous data. 10. Theory of parametric and non-parametric hypotheses, errors of the first and second kind. 11. The basic principle of the F-test, including its use in practice. 12. The basic principle of t-tests, for cases of the same (different) variances, including their use in practice. 13. The basic principle of the method of least squares, linear regression. 14. Confidence intervals for the regression line.
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Learning activities and teaching methods
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- Preparation for examination
- 150 hours per semester
- Preparation for examination
- 150 hours per semester
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| prerequisite |
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| Knowledge |
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| In order to successfully master the subject of statistics, it is important that the student has certain professional knowledge and skills before starting the course. Such knowledge and skills should include: Basic Mathematics: The student should have a solid foundation in basic mathematics, including knowledge of algebraic operations, arithmetic, matrices, and basic mathematical functions. Knowledge of Mathematical Symbolism: The ability to read and write mathematical expressions and symbols is important because statistics uses mathematical notation. Probability and Statistics: Knowledge of basic probability concepts such as probability distribution, mean, variance, covariance and correlation is key. Understanding Data: A basic understanding of what data is, how it is obtained, and how it is organized is helpful. Analytical Thinking: The student should have the ability to think logically and analytically, which is important for unraveling statistical problems and situations. Fundamentals of Statistical Methods: An awareness of the existence and function of basic statistical methods such as mean, median, quartiles, standard deviation is useful. Basics Working with Software: If the student has previous experience working with computers and software, especially with spreadsheets, it can be an advantage. English Language: The ability to read and understand English texts is important because many statistical materials are available in the English language. Working with Data: Knowing the basics of working with data, such as collecting, organizing and cleaning data, can be helpful. Logical Thinking and Problem Solving: The ability to formulate and solve problems is key to the effective use of statistical methods. These are the basic professional knowledge and skills that students will benefit from acquiring before studying statistics. If the student does not have this knowledge, additional training or courses may be needed to be prepared for the subject of statistics. |
| In order to successfully master the subject of statistics, it is important that the student has certain professional knowledge and skills before starting the course. Such knowledge and skills should include: Basic Mathematics: The student should have a solid foundation in basic mathematics, including knowledge of algebraic operations, arithmetic, matrices, and basic mathematical functions. Knowledge of Mathematical Symbolism: The ability to read and write mathematical expressions and symbols is important because statistics uses mathematical notation. Probability and Statistics: Knowledge of basic probability concepts such as probability distribution, mean, variance, covariance and correlation is key. Understanding Data: A basic understanding of what data is, how it is obtained, and how it is organized is helpful. Analytical Thinking: The student should have the ability to think logically and analytically, which is important for unraveling statistical problems and situations. Fundamentals of Statistical Methods: An awareness of the existence and function of basic statistical methods such as mean, median, quartiles, standard deviation is useful. Basics Working with Software: If the student has previous experience working with computers and software, especially with spreadsheets, it can be an advantage. English Language: The ability to read and understand English texts is important because many statistical materials are available in the English language. Working with Data: Knowing the basics of working with data, such as collecting, organizing and cleaning data, can be helpful. Logical Thinking and Problem Solving: The ability to formulate and solve problems is key to the effective use of statistical methods. These are the basic professional knowledge and skills that students will benefit from acquiring before studying statistics. If the student does not have this knowledge, additional training or courses may be needed to be prepared for the subject of statistics. |
| Skills |
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| In order to successfully master the subject of statistics, it is assumed that the student has certain professional skills and abilities before starting classes. These skills and abilities include: Mathematical Skills: The student should be able to perform basic mathematical operations such as addition, subtraction, multiplication and division, including using variables and symbols. Knowledge of Probabilistic Thinking: The student should be able to understand probabilistic concepts such as random events, probability distributions, and probabilistic modeling. Ability to Work with Data: The student should be able to collect, organize and analyze data. This includes the ability to create tables, graphs and statistical outputs. Statistical Analysis: The student should be able to perform basic statistical analyses, including the calculation of mean, median, quartiles, standard deviation and correlation. Skill in Logical Thinking: The student should be able to formulate logical arguments and solve statistical problems. Critical Thinking Ability: The student should be able to critically evaluate statistical results and recognize possible errors or distortions. Working with Statistical Software: The student should be able to work with statistical software such as R, Python with statistics libraries (eg numpy, scipy, pandas) or statistical packages such as SPSS or SAS. Communication of Results: The student should be able to clearly communicate his statistical results and conclusions both orally and in writing. Basic Knowledge of Statistical Concepts: The student should have a basic understanding of concepts such as probability, mean, variance, parameter estimation, hypothesis testing and confidence intervals. Ability to Work in a Team: Statistical work can often involve working with colleagues, so it is important to have the ability to communicate effectively and work in a team. These professional skills and abilities are crucial for the successful study of statistics and the effective use of statistical methods in study and work situations. If a student does not provide these skills prior to studying statistics, it may be helpful to receive additional preparation or support to prepare them for the subject. |
| In order to successfully master the subject of statistics, it is assumed that the student has certain professional skills and abilities before starting classes. These skills and abilities include: Mathematical Skills: The student should be able to perform basic mathematical operations such as addition, subtraction, multiplication and division, including using variables and symbols. Knowledge of Probabilistic Thinking: The student should be able to understand probabilistic concepts such as random events, probability distributions, and probabilistic modeling. Ability to Work with Data: The student should be able to collect, organize and analyze data. This includes the ability to create tables, graphs and statistical outputs. Statistical Analysis: The student should be able to perform basic statistical analyses, including the calculation of mean, median, quartiles, standard deviation and correlation. Skill in Logical Thinking: The student should be able to formulate logical arguments and solve statistical problems. Critical Thinking Ability: The student should be able to critically evaluate statistical results and recognize possible errors or distortions. Working with Statistical Software: The student should be able to work with statistical software such as R, Python with statistics libraries (eg numpy, scipy, pandas) or statistical packages such as SPSS or SAS. Communication of Results: The student should be able to clearly communicate his statistical results and conclusions both orally and in writing. Basic Knowledge of Statistical Concepts: The student should have a basic understanding of concepts such as probability, mean, variance, parameter estimation, hypothesis testing and confidence intervals. Ability to Work in a Team: Statistical work can often involve working with colleagues, so it is important to have the ability to communicate effectively and work in a team. These professional skills and abilities are crucial for the successful study of statistics and the effective use of statistical methods in study and work situations. If a student does not provide these skills prior to studying statistics, it may be helpful to receive additional preparation or support to prepare them for the subject. |
| learning outcomes |
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| Knowledge |
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| Basic Mathematics: A strong foundation in mathematics is essential. This includes algebra, differential and integral calculus, linear algebra and sets. |
| Basic Mathematics: A strong foundation in mathematics is essential. This includes algebra, differential and integral calculus, linear algebra and sets. |
| Probability: Concepts of probability are central to statistics. Students should understand probability distributions, mean, variance, and other probability concepts. |
| Probability: Concepts of probability are central to statistics. Students should understand probability distributions, mean, variance, and other probability concepts. |
| Statistical Methods: Students should be familiar with various statistical methods, including descriptive statistics, inferential statistics, regression, analysis of variance, and others. |
| Statistical Methods: Students should be familiar with various statistical methods, including descriptive statistics, inferential statistics, regression, analysis of variance, and others. |
| Theory of Statistics: The study of statistics requires an understanding of the theoretical foundations of statistical methods and concepts such as sampling, parameter estimation, hypothesis testing, and confidence intervals. |
| Theory of Statistics: The study of statistics requires an understanding of the theoretical foundations of statistical methods and concepts such as sampling, parameter estimation, hypothesis testing, and confidence intervals. |
| Statistical Software: Students should be able to work with statistical software such as R, Python with statistics libraries (eg numpy, scipy, pandas) or statistical packages such as SPSS or SAS. |
| Statistical Software: Students should be able to work with statistical software such as R, Python with statistics libraries (eg numpy, scipy, pandas) or statistical packages such as SPSS or SAS. |
| Data Analysis: Knowledge of data analysis methods, including techniques for data visualization and pattern identification, is essential. |
| Data Analysis: Knowledge of data analysis methods, including techniques for data visualization and pattern identification, is essential. |
| Mathematical Statistics: Students should have knowledge of advanced concepts in mathematical statistics such as convergence, asymptotic properties of estimates and tests, maximum likelihood theory, Bayesian statistics, etc. |
| Mathematical Statistics: Students should have knowledge of advanced concepts in mathematical statistics such as convergence, asymptotic properties of estimates and tests, maximum likelihood theory, Bayesian statistics, etc. |
| Working with Real Data: Students should have experience working with real data, including data collection, data cleaning and data interpretation. |
| Working with Real Data: Students should have experience working with real data, including data collection, data cleaning and data interpretation. |
| Statistical Consulting: The ability to communicate statistical results and consult with others in a variety of industries is important if you pursue statistics in a business or academic setting. |
| Statistical Consulting: The ability to communicate statistical results and consult with others in a variety of industries is important if you pursue statistics in a business or academic setting. |
| Ethics and Responsibility in Statistics: Students should be familiar with the ethical aspects of working with data, including the protection of privacy and the responsible use of statistical methods. |
| Ethics and Responsibility in Statistics: Students should be familiar with the ethical aspects of working with data, including the protection of privacy and the responsible use of statistical methods. |
| Skills |
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| Basic Understanding of Statistics: Students will learn the basics of statistics, including concepts such as probability, probability distributions, statistical tests and their interpretation. |
| Basic Understanding of Statistics: Students will learn the basics of statistics, including concepts such as probability, probability distributions, statistical tests and their interpretation. |
| Data Acquisition: Students will learn how to acquire data relevant to technical quality management. This may include data collection and sampling techniques. |
| Data Acquisition: Students will learn how to acquire data relevant to technical quality management. This may include data collection and sampling techniques. |
| Data Analysis: Students will learn to use various statistical methods to analyze data. This includes descriptive statistics, inferential statistics and regression analysis. |
| Data Analysis: Students will learn to use various statistical methods to analyze data. This includes descriptive statistics, inferential statistics and regression analysis. |
| Quality Control: Students will learn about quality control methods such as statistical process control (SPC), control charts, and methods for detecting and solving quality problems. |
| Quality Control: Students will learn about quality control methods such as statistical process control (SPC), control charts, and methods for detecting and solving quality problems. |
| Importance in Industry: Students will realize how statistical analysis contributes to effective quality management in industry. They will be able to identify areas where statistics can be applied to improve processes and reduce errors. |
| Importance in Industry: Students will realize how statistical analysis contributes to effective quality management in industry. They will be able to identify areas where statistics can be applied to improve processes and reduce errors. |
| Software Applications: Students will learn to work with statistical software, enabling them to perform data analyzes and generate relevant statistical outputs. |
| Software Applications: Students will learn to work with statistical software, enabling them to perform data analyzes and generate relevant statistical outputs. |
| Communication of Results: An important part of this course will be the way in which students present and communicate the results of their statistical analyses, as this information is important for the decision-making process in technical quality management. |
| Communication of Results: An important part of this course will be the way in which students present and communicate the results of their statistical analyses, as this information is important for the decision-making process in technical quality management. |
| Practical Examples: The course will include real examples and studies that will enable students to apply their knowledge and skills to specific situations in the field of technical quality management. |
| Practical Examples: The course will include real examples and studies that will enable students to apply their knowledge and skills to specific situations in the field of technical quality management. |
| teaching methods |
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| Knowledge |
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| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Dialogic (Discussion, conversation, brainstorming) |
| Dialogic (Discussion, conversation, brainstorming) |
| Skills |
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| Simple experiments |
| Simple experiments |
| Practice exercises |
| Practice exercises |
| assessment methods |
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| Knowledge |
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| Analysis of works made by the student (Technical products) |
| Analysis of works made by the student (Technical products) |
| Oral examination |
| Oral examination |
| Written examination |
| Written examination |
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Recommended literature
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DUPAČ, V. Pravděpodobnost a matematická statistika. 2. upr. vyd.. Praha: Karolinum, 2013. ISBN 978-80-246-2208-8.
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HEBÁK, P. Statistické myšlení a nástroje analýzy dat. 1. vyd.. Praha: Informatorium, 2013. ISBN 978-80-7333-105-4.
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HENDL, J. Přehled statistických metod zpracování dat: Analýza a Meta analýza dat. Praha, 2004. ISBN 80-7178-820-1.
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MELOUN, M., MILITKÝ, J. Kompendium statistického zpracování dat. Praha: Karolinum, 2012. ISBN 978-80-246-2196-8.
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MONTGOMERY, D.C. Introduction to Statistical Quality Control. 5th Ed.. Hoboken: John Wiley, 2005. ISBN 0471661228.
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NENADÁL, J. Měření v systémech managementu jakosti. Praha: Management Press, 2004. ISBN 80-7261-110-0.
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PATA, V., KUBIŠOVÁ, M. Statistické metody hodnocení jakosti strojírenských povrchů. Zlín: FT UTB, 2018. ISBN 978-80-7454-740-9.
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TOŠENOVSKÝ, J. Statistické metody pro zlepšování jakosti. Ostrava: Montanex, 2000. ISBN 80-7225-040-X.
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ZVÁRA, K. Pravděpodobnost a matematická statistika. 6. vyd.. Praha: Matfyzpress, 2019. ISBN 978-80-7378-388-4.
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