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.
2.1 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.
7.1 Introduction to linear regression.
7.2 Simple regression.
Estimation of parameters. Significance and interpretation
7.3 Multiple regression.
Estimation of parameters, significance and interpretation
7.4 Regression with qualitative variables (dichotomous / polytomous).