1.Descriptive statistics
1.1. Qualitative and quantitative data
1.2. Univariate descriptive statistics. Frequency tables
1.2.1. Graphical representation for qualitative data: Bar chart, pie chart, Pareto diagram
1.2.2. Graphical representation for quantitative data: Histograms, frequency polygons, boxplots
1.2.3. Analytical measures for data summary
1.2.3.1. Measures of central tendency: Average, median and mode
1.2.3.2. Measures of variability: Variance, coefficient of variation, quartiles and percentiles
1.2.3.3. 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 probability
2.4. Independence and conditional probability
2.5. Law of total probability
2.6. Bayes theorem
3. Introduction to random variables
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
4. Univariate distribution models
4.1. Probability models for discrete random variables. Bernoulli, Binomial, geometric and Poisson
4.2. Probability models for continuous random variables. Uniform, exponential and normal distributions. The central limit theorem
5. Introduction to statistical inference
5.1. Population and sample. Distribution of the sample mean
5.2. Confidence intervals for the sample mean
5.3. Distributional inference of a population using a sample
6. Hypothesis Testing
6.1 Population and sample (review)
6.2 Null hypothesis and alternative hypothesis
6.3 Hypothesis testing for one population
6.4. Hypothesis testing for the mean, proportion and variance of one population
6.5. Hypothesis testing for two populations: Difference of means and proportions
7. Quality control
7.1. Introduction to quality control. Assignable and non-assignnable causes
7.2. Control charts for variables. Control charts for the mean and range. Process capability.
7.2.1. Control charts for the mean
7.2.2. Control charts for the range
7.2.3. Control charts for the mean for the standard deviation
7.2.4. Process capability. Probability of defective products
7.3. Control charts for attributes
7.3.1. p control chart
7.3.2. np control chart
8. Regression
8.1 Introduction to linear regression
8.2 Simple linear regression
8.2.1. Hypothesis
8.2.2. Parameter estimation
8.2.3. Parameter significance and interpretation
8.2.4. Model diagnosis
8.3. Multiple linear regression
8.3.1. Hypothesis
8.3.2. Parameter estimation
8.3.3. Parameter significance and interpretation
8.3.4. Model diagnosis
8.3.5. Multicollinearity
8.3.6. Regression with qualitative variables (dichotomous / polytomous).