639-3021/01 – Foundations of Mathematical Statistics (ZMS)

Gurantor departmentDepartment of Quality ManagementCredits4
Subject guarantorIng. Filip Tošenovský, Ph.D.Subject version guarantorIng. Filip Tošenovský, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageEnglish
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
TOS012 Ing. Filip Tošenovský, Ph.D.
TOS40 prof. RNDr. Josef Tošenovský, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Knowledge of basic statistical methods Analysis of real data Ability to process correctly experimental data Managing work with Excel

Teaching methods



The primary aim of the subject is an exposition of the theory of estimation of population parameters, hypothesis testing, modelling of technological processes with regression models and their assessment by correlation analysis. Multivariate regression is taught under the required theoretical conditions. Correlation analysis shows ways of measuring dependence for various types of variables.

Compulsory literature:

JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7. DRAPER, N. R. and H. SMITH. Applied Regression Analysis. NY: Wiley, 1998. ISBN 978-0471170822. RYAN, T. P. Modern Regression Methods. NY: Wiley, 2008. ISBN 978-0470550441. ASHENFELTER, O. B.,P. B. LEVINE and D. J. ZIMMERMAN. Statistics and Econometrics: Methods and Applications. NY: Wiley, 2006. ISBN-13: 978-0470009451.

Recommended literature:

MONTGOMERY, D. C. Applied Statistics and Probability for Engineers. NY: Wiley, 2010. ISBN-13 978-1-1185-3971-2. SHESKIN, D. J. Handbook of Parametric and Nonparametric Statistical Procedures. NY: Chapman and Hall, 2003. ISBN 1-58488-440-1.

Way of continuous check of knowledge in the course of semester

Two tests in the course of the semester, where the score is counted towards the cumulative credit points. One project, where the score is counted towards the cumulative credit points. The examination is in written form.


Other requirements

80% attendance in seminars


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1. Introduction to statistics – explanation of its use in metallurgy. Graphical representation of data samples, assessment of data type. General principles of testing. 2. Confirmation of data sample homogeneity using graphs. Outliers – their depiction, detection (box plot) and solution. 3. Confirmation of data independence using graphs. Effect of data dependence on quality of data sample processing. 4. Confirmation of normality: normal distribution, Gauss curve and its parameters, empirical histogram. Reasons why normality is required, and procedures to be followed if the normality condition is not met. 5. Descriptive characteristics of location, variability, skewness and kurtosis. The notion of robustness of numerical characteristics. 6. Student’s distribution, Fisher’s distribution, Pearson’s distribution and their graphs. Examples of using the distributions. Use of tables of quantiles and critical values. 7. Point estimation and confidence intervals. „Confidence level“ and „nivel of test“. 8. Analysis of two data samples. Testing the difference of expected values and variances. Two-sample t-test, F-test. 9. Evaluating a measure of dependence (correlation) of two variables: Pearson’s correlation coefficient, Spearman’s rank correlation coefficient. 10. Regression analysis – simple (paired) linear regression. Estimation of regression coefficients by least squares. Assessment of significance and quality of the regression function. Simple nonlinear regression models (power, exponential, logarithmic, quadratic and polynomial models). 11. Regression analysis – multivariate linear regression. Assessment of significance of the model and its regression coefficients. Use of multivariate regression.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40  20
        Examination Examination 60  31
Mandatory attendence parzicipation: 70% attendance at the seminar

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0413A270003) Quality Management and Control of Industrial Systems MPZ P English Ostrava 1 Compulsory study plan
2021/2022 (N0413A270003) Quality Management and Control of Industrial Systems MPZ P English Ostrava 1 Compulsory study plan
2020/2021 (N0413A270003) Quality Management and Control of Industrial Systems MPZ P English Ostrava 1 Compulsory study plan
2019/2020 (N0413A270003) Quality Management and Control of Industrial Systems MPZ P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
FMT + Nanotechnology 2022/2023 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block