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Mathematical Statistics

Course developer

Course abstract

The study course gives introduction to the basics of mathematical statistics, emphasizing its importance for studies and application to interpret scientific investigations, experiments and data. Students gain an understanding of statistical methods for obtaining logical conclusions by exploring various kinds of random phenomena. The course covers sampling distributions, and hypothesis testing with emphasis on comparing of mean values and analysis of statistical relationship.

Learning outcomes and their assessment

After the study course students will have: knowledge and understanding of the classification and basic principles of the choice of mathematical statistical methods according to tasks of the research (laboratory works); skills to apply mathematical statistical methods for course projects and diploma, as well as professional research tasks (laboratory works, tests); competence to analyse, systematize data processing results and use them for evaluation of cadastre and real estate (independent work).

Course Content(Calendar)

Full-time studies:
1. The role of statistics in engineering. Application of mathematical methods in land surveying (2h).
2. Random variables and probability distributions (2h).
3. Random sampling and data description (2h).
4. Types of descriptive statistics (2h).
5. Evaluation of population parameters. Statistical hypotheses. Classification of statistical tests (2h).
6. Test Nr.1 (2h).
7. Normal distribution law (2H).
8. t-test for dependent samples (2h).
9. t-test for independent samples and Fisher's F test (2h).
10. Test Nr.2 (2h).
11. Analysis of correlation (2h).
12. Simple linear regression analysis (2h).
13. Basics of nonlinear regression (2h).
14. χ2 as a statistical independence test (2h).
15. Non-parametric statistical methods (2h).
16. Test Nr.3 (2h).
Part-time studies:
All topics specified for full-time studies are implemented, but the number of contact hours is 1/2 of the specified number of hours

Requirements for awarding credit points

3 tests during the course;
submission of independent work results.

Description of the organization and tasks of students’ independent work

During the semester the student has to perform independent work. The work must be written and submitted electronically on the e-learning site.

Criteria for Evaluating Learning Outcomes

Cumulative course grade will be determined during the semester by the relative weights given:
independent work – 10%;
test Nr. 1 – 30%;
test Nr. 2 – 30%;
test Nr. 3 – 30%.

Compulsory reading

1. Arhipova I., Bāliņa S. Statistika ekonomikā un biznesā. Rīga: Datorzinību Centrs, 2006. 362 lpp.
2. Arhipova I., Bāliņa S. Statistika ekonomikā. Risinājumi ar SPSS un Microsoft Excel. Rīga: Datorzinību Centrs, 2003. 349 lpp.
3. Smotrovs J. Varbūtību teorija un matemātiskā statistika. II Rīga: Zvaigzne ABC, 2007.
4. Grīnglazs L., Kopitovs J. Matemātiskā statistika: ar datoru lietojuma paraugiem uzdevumu risināšanai. Rīga: Rīgas Starptautiskās ekonomikas un biznesa administrācijas augstskola, 2003.

Further reading

1. Krastiņš O. Ciemiņa I. Statistika. Rīga: LR Centrālā statistikas pārvalde, 2003. 267 lpp.
2. Krastiņš O. Statistika un ekonometrija. Rīga: LR Centrālā statistikas pārvalde, 1998. 435 lpp.

Periodicals and other sources

Centrālās statistikas pārvaldes mājas lapa [tiešsaiste]. Pieejams: https://www.csb.gov.lv

Notes

Professional higher education bachelor study program "Land Management and Surveying" full-time studies and part-time studies