Study Guide

Objective

After completing the course the student can:
- calculate different mean and standard deviation figures for a given statistical data
- determine the regression line and correlation, and understand their significance
- identify and draw various statistical diagrams
- recognize the basic concepts of continuous and discrete probability distributions
- normalize a normally distributed variable and calculate the associated probabilities
- calculate confidence intervals and understand the significance of error in statistical mathematics
- determine p-value using the z-test and t-test of average
- construct contingency tables and apply the chi-square test

Content

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät
Laskinohjelmistojen ohjeet
Harjoituskoe

Teaching methods

Luennot
Laskuharjoitukset
Kokeet
Vapaaehtoinen harjoitustyö

Exam schedules

Tilastot-osio:
osakoe ja sen uusinta hiihtoloman jälkeen.
Todennäköisyys-osio:
osakoe ja sen uusinta ennen huhtikuun lopulla.

Lopullinen uusinta toukokuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Completion alternatives

Vapaaehtoinen harjoitustyö, + 2op

Student workload

14*2h luennot
14*1h laskuharjoitukset
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua
vapaaehtoinen harjoitustyö, + 2op

Content scheduling

Tilastot:
- Tilastomuuttuja
- Keskiluvut ja hajontaluvut
- Diagrammien piirtäminen
- Regressio
- Korrelaatio

Todennäköisyys:
- Todennäköisyyden peruskaavat
- Diskreetti satunnaismuuttuja
- Binomijakauma ja Poisson-jakauma
- Jatkuva satunnaismuuttuja
- Normaalijakauma ja normittaminen
- Tilastollinen testaaminen
- Keskiarvo z-testi ja t-testi, khiiNeliö-riippumattomuustesti

Further information

Sähköposti.

Evaluation scale

H-5

Assessment methods and criteria

Arvosana määräytyy kokeista saadun yhteispistemäärän (max. 16+16=32) ja kotitehtävistä saadun pistemäärän (max. 10) perusteella seuraavan taulukon mukaisesti (kokeista täytyy saada yhteensä vähintään 12 pistettä päästäkseen läpi kurssista):
0-11: 0
12-17: 1
18-23: 2
24-29: 3
30-35: 4
36-42: 5

Assessment criteria, fail (0)

Arvosanataulukon mukaan.

Assessment criteria, satisfactory (1-2)

Arvosanataulukon mukaan.

Assessment criteria, good (3-4)

Arvosanataulukon mukaan.

Assessment criteria, excellent (5)

Arvosanataulukon mukaan.

Qualifications

Courses Engineering Precalculus, Calculus and Topics in Applied Mathematics
OR
equivalent skills

Objective

After completing the course the student can:
- calculate different mean and standard deviation figures for a given statistical data
- determine the regression line and correlation, and understand their significance
- identify and draw various statistical diagrams
- recognize the basic concepts of continuous and discrete probability distributions
- normalize a normally distributed variable and calculate the associated probabilities
- calculate confidence intervals and understand the significance of error in statistical mathematics
- determine p-value using the z-test and t-test of average
- construct contingency tables and apply the chi-square test

Content

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Materials

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in ITSLEARNING.

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the mean and standard deviation,.. , and the figures to analyze the data.
The students will team up for a project work and writing reports on some current and relevant aspect of statistics, which gives everyone an opportunity to understand the topic; all students will develop their statistical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Completion alternatives

Probability and Statistics (3rd edition),Murray R. Spiegel, John J. Schiller, R. Alu Srinivasan, SCHAUM’S outlines.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in TSLEARNING): peer feedback summative teacher feedback at the end of the course.
Two written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Courses Engineering Precalculus, Calculus and Topics in Applied Mathematics
OR
equivalent skills

Objective

After completing the course the student can:
- calculate different mean and standard deviation figures for a given statistical data
- determine the regression line and correlation, and understand their significance
- identify and draw various statistical diagrams
- recognize the basic concepts of continuous and discrete probability distributions
- normalize a normally distributed variable and calculate the associated probabilities
- calculate confidence intervals and understand the significance of error in statistical mathematics
- determine p-value using the z-test and t-test of average
- construct contingency tables and apply the chi-square test

Content

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät ja mallivastaukset
Laskinohjelmistojen ohjeet
Harjoituskoe

Teaching methods

Luennot
Laskuharjoitukset
Kokeet
Vapaaehtoinen harjoitustyö

Exam schedules

Tilastot:
Osakoe ja sen uusinta ennen syyslomaa
Todennäköisyys:
Osakoe ja sen uusinta ennen joululomaa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Completion alternatives

Pelkät osakokeet ilman pisteitä laskuharjoituksista
Vapaaehtoinen harjoitustyö, + 2op

Student workload

16*2h luennot
8*2h laskuharjoitukset, joissa yhteensä noin 8*12 kpl tehtäviä
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua
vapaaehtoinen harjoitustyö, 2op

Content scheduling

Elokuu-lokakuu, tilastot:
- Tilastomuuttuja
- Keskiluvut ja hajontaluvut
- Diagrammien piirtäminen
- Regressio
- Korrelaatio
- Virhetyypit

Lokakuu-joulukuu, todennäköisyys:
- Todennäköisyyden peruskaavat
- Diskreetti satunnaismuuttuja
- Binomijakauma ja Poisson-jakauma
- Jatkuva satunnaismuuttuja
- Normaalijakauma ja normittaminen
- Tilastollinen testaaminen
- Keskiarvo z-testi ja t-testi, khiiNeliö-riippumattomuustesti

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa.
Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, good (3-4)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, excellent (5)

Arvosanataulukko löytyy ITSL-sivulta.

Qualifications

Courses Engineering Precalculus, Calculus and Topics in Applied Mathematics
OR
equivalent skills

Objective

After completing the course the student can:
- calculate different mean and standard deviation figures for a given statistical data
- determine the regression line and correlation, and understand their significance
- identify and draw various statistical diagrams
- recognize the basic concepts of continuous and discrete probability distributions
- normalize a normally distributed variable and calculate the associated probabilities
- calculate confidence intervals and understand the significance of error in statistical mathematics
- determine p-value using the z-test and t-test of average
- construct contingency tables and apply the chi-square test

Content

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Materials

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in ITSLEARNING.

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the mean and standard deviation,.. , and the figures to analyze the data.
The students will team up for a project work and writing reports on some current and relevant aspect of statistics, which gives everyone an opportunity to understand the topic; all students will develop their statistical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Completion alternatives

Probability and Statistics (3rd edition),Murray R. Spiegel, John J. Schiller, R. Alu Srinivasan, SCHAUM’S outlines.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Courses Engineering Precalculus, Calculus and Topics in Applied Mathematics
OR
equivalent skills

Objective

After completing the course the student can:
- calculate different mean and standard deviation figures for a given statistical data
- determine the regression line and correlation, and understand their significance
- identify and draw various statistical diagrams
- recognize the basic concepts of continuous and discrete probability distributions
- normalize a normally distributed variable and calculate the associated probabilities
- calculate confidence intervals and understand the significance of error in statistical mathematics
- determine p-value using the z-test and t-test of average
- construct contingency tables and apply the chi-square test

Content

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät ja mallivastaukset
Laskinohjelmistojen ohjeet
Harjoituskoe

Teaching methods

Luennot
Laskuharjoitukset
Kokeet
Vapaaehtoinen harjoitustyö

Exam schedules

Tilastot:
Osakoe ja sen uusinta ennen syyslomaa
Todennäköisyys:
Osakoe ja sen uusinta ennen joululomaa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Completion alternatives

Pelkät osakokeet ilman pisteitä laskuharjoituksista
Vapaaehtoinen harjoitustyö, + 2op

Student workload

16*2h luennot
8*2h laskuharjoitukset, joissa yhteensä noin 8*12 kpl tehtäviä
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua
vapaaehtoinen harjoitustyö, 2op

Content scheduling

Elokuu-lokakuu, tilastot:
- Tilastomuuttuja
- Keskiluvut ja hajontaluvut
- Diagrammien piirtäminen
- Regressio
- Korrelaatio
- Virhetyypit

Lokakuu-joulukuu, todennäköisyys:
- Todennäköisyyden peruskaavat
- Diskreetti satunnaismuuttuja
- Binomijakauma ja Poisson-jakauma
- Jatkuva satunnaismuuttuja
- Normaalijakauma ja normittaminen
- Tilastollinen testaaminen
- Keskiarvo z-testi ja t-testi, khiiNeliö-riippumattomuustesti

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa.
Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, good (3-4)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, excellent (5)

Arvosanataulukko löytyy ITSL-sivulta.

Qualifications

Courses Engineering Precalculus, Calculus and Topics in Applied Mathematics
OR
equivalent skills

Objective

After completing the course the student can:
- calculate different mean and standard deviation figures for a given statistical data
- determine the regression line and correlation, and understand their significance
- identify and draw various statistical diagrams
- recognize the basic concepts of continuous and discrete probability distributions
- normalize a normally distributed variable and calculate the associated probabilities
- calculate confidence intervals and understand the significance of error in statistical mathematics
- determine p-value using the z-test and t-test of average
- construct contingency tables and apply the chi-square test

Content

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Materials

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in ITSLEARNING.

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the mean and standard deviation,.. , and the figures to analyze the data.
The students will team up for a project work and writing reports on some current and relevant aspect of statistics, which gives everyone an opportunity to understand the topic; all students will develop their statistical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Completion alternatives

Probability and Statistics (3rd edition),Murray R. Spiegel, John J. Schiller, R. Alu Srinivasan, SCHAUM’S outlines.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

- mean and standard deviation figures
- diagrams and their differences
- regression, correlation
- basic definitions and formulas of probability
- discrete probability distribution, binomial distribution, Poisson distribution
- continuous probability distribution, normal distribution, normalization
- statistical testing, sampling, confidence interval
- z-test and t-test of average
- contingency tables and chi-square test

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Courses Engineering Precalculus, Calculus and Topics in Applied Mathematics
OR
equivalent skills