Statistics

Statistics (222 - 13986)
Study: Bachelor in Electrical Power Engineering
Semester 2/Spring Semester
1st Year Course/Lower Division

Please note: this course is cross-listed under the majority of engineering departments. Students should select the course from the department that best fits their area of study.

Students are expected to have completed:

Calculus I
Algebra

Compentences and Skills that will be Acquired and Learning Results:

In today's world there is an enomous amount of available information. There are diverse sources and many of them are accessible through the Internet. To analyze this information and draw valid conclusions we need to use some specific techniques. Statistics is the most widely used and the most successful technique. In this course we will learn how to obtain information from the data with techniques that you will use both in your studies and in your professional career, because these techniques are commonly used by most companies and organizations.

Today a statistical analysis is inconceivable without computer resources. Therefore the teaching of Statistics will rely heavily on computer practices and a part of the final exam will be held in a computer classroom.

After completing this course, you should be able to extract information from the data and to express those conclusions in a written report. Also, you can establish relationships between variables using the regression model and to interpret the model properly.

Description of Contents: Course Description
Topics:
1. Descriptive Statistics
1.1 Qualitative and Quantitative data.
1.2 Univariate Descriptive Statistics.
1.2.1 Summary of data using frequency tables.
1.2.2 Graphical representation of data.
¿ Graphical representation for qualitative data:
Bar chart, pie chart, Pareto diagram.
¿ Graphical representation for quantitative data:
Histograms, frequency polygons, boxplots.
1.2.3 Analytical measures for data summary.
¿ Measures of central tendency: Average, median and mode.
¿ Measures of variability: Variance, Coefficient of Variation, Median, Quartiles and Percentiles.
¿ Other Measures: Skewness and kurtosis.
1.3 Descriptive statistics for two variables.
Scatter plots. Covariance and correlation.

2. Probability
2.1 Introduction to the concept of probability:
¿ Equiprobability and Laplace rule.
¿ Frequentist approach and law of large numbers.

2.2 Events and operations with events.

Event definition. Venn diagrams. Union, Intersection and complementary events.

2.3 Definition and properties of the probability.
2.4 Independence and conditional probability.
2.5 law of total probability.
2.6 Bayes Theorem.

3. Random variables and probability models
3.1 Definition of random variable (discrete / continuous) and properties. Probability function, density function.
3.2 Expectation and variance of discrete and continuous random variables.
3.3 Distribution function.
3.4 Probability Models for discrete random variables. Bernoulli, Binomial.
3.5 Probability Models for continuous random variables. The normal distribution. The central limit theorem.
4. Statistical Inference
4.1 Introduction to statistical inference.
Population and sample. Distribution of the sample mean.
4.2 Confidence intervals for the sample mean.
5. Hypothesis Testing
5.1 Population and sample (review).
5.2 Null hypothesis and alternative hypothesis.
5.3 Hypothesis testing for the mean, proportion and variance of one population.
5.4 Hypothesis testing for two populations: Difference of means and proportions.

6. Quality control
6.1 Introduction to quality control
6.2 Control charts for variables. Control charts for the mean and range. Process capability.
6.3 Control charts for attributes. P and np control charts.

7. Regression
7.1 Introduction to linear regression.
7.2 Simple regression.
Hypothesis.
Estimation of parameters. Significance and interpretation
Diagnosis.
7.3 Multiple regression.
Hypothesis.
Estimation of parameters, significance and interpretation
Diagnosis
Multicollinearity
7.4 Regression with qualitative variables (dichotomous / polytomous).

Learning Activities and Methodology:

- Lecture: 2,5 ECTS
- Problem solving sessions (in small groups): 1,5 ECTS
- Computes sessions (consistent of individual work out of the classroom with programmed tutorial sessions) 1,5 ECTS
- Evaluation sessions (continuos evaluation, some of them at computes laboratories): 0,5 ECTS

Assessment System:

The final grade will be computed giving a 50% weight to the grade in the final exam and a 50% weight to the continuous evaluation grade. A minimum of 5 points on the final exam will be required.

The continuous evaluation consists of a midterm theoretical exam and a practice exam. The midterm exam will render 10% of the final grade, while the practice exam will render 40%. You have to present the practice workbook and take the practice exam. Without any of these two things, the grade in the practice part of the course will be 0.

Summarizing:

10% Midterm theoretical exam
40% Practice workbook + Practice exam (May)
50% Final exam

The assessment system applied to the students that have not followed the continuous will be the most favourable to the student under the University rules.

Basic Bibliography:

PEREZ, C.. "Estadística práctica con Statgraphics". 2000.
PEÑA, D. Y ROMO, J.. "Introducción a la Estadística para las Ciencias Sociales". McGraw-Hill.