Statistics is currently used in almost all fields of knowledge, particularly in the sciences. Statistics is a branch of mathematics concerned with the theory, procedures and methodology used to analyse data, with variability and uncertainty being inherent to its nature. There are numerous applications of statistics, such as in aerospace engineering. The aim of this course in statistics for aerospace engineering is to provide students with the necessary skills to understand statistics as applied to aerospace engineering.
Cross-cutting
Big Data
8 pm
Fundamentals of Statistics
Big Data
8 pm
Introduction
Objectives
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To understand the basic concepts of statistics, its functions and how data is measured.
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To interpret statistical graphs and scientific notation correctly.
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Define the types of statistics and their variables, and distinguish between the different types of events and the sampling method to be used.
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To understand probability distributions and their different types, and to use the necessary tools to apply them.
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To describe the Central Limit Theorem and its proof, and to understand its development throughout history.
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Test hypotheses using the appropriate method and define the parameters for identifying them.
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To understand linear regressions and how to choose them depending on the type of variable, as well as to select the most appropriate variables for building a regression model and for its subsequent validation and interpretation.
Table of Contents
TEACHING UNIT 1. Basic concepts and data organisation
1. An introduction to statistics
2. The concept and functions of statistics
2.1. Descriptive statistics
2.2. Inferential statistics
3. Measurement and scales of measurement
3.1. Nominal scale
3.2. Ordinal scale
3.3. Interval scale
3.4. Ratio scale
4. Variables: Classification and notation
5. Frequency distribution
5.1. Frequency distribution by intervals
6. Graphical representations
Glossary
TEACHING UNIT 2. Basic descriptive statistics and inference
1. Descriptive statistics
1.1. Description of a qualitative variable
1.2. Description of a quantitative variable
2. Inferential statistics
2.1. Prerequisite concepts
2.2. Sampling methods
2.3. Key indicators
Glossary
TEACHING UNIT 3. Probability distributions
1. Basic concepts of probability
2. Discrete probability variables
2.1. Probability function
2.2. Distribution function
2.3. Mean and variance of a random variable
3. Discrete probability distributions
3.1. The binomial distribution
3.2. Other discrete distributions
4. Normal distribution
5. Distributions associated with the normal distribution
5.1. Pearson’s “chi-squared” distribution
5.2. Student’s “t” distribution
Glossary
TEACHING UNIT 4. The Central Limit Theorem
1. Introduction to the Central Limit Theorem
2. Normal approximation to the binomial distribution
2.1. First version of the Central Limit Theorem
2.2. Use of the normal approximation to the binomial distribution
3. Laplace’s Central Limit Theorem
4. The Central Limit Theorem and the first rigorous proofs
4.1. Liapunov’s Central Limit Theorem
4.2. Lindeberg’s Central Limit Theorem
4.3. The Lindeberg–Lévy Central Limit Theorem
4.4. The Lindeberg–Feller Central Limit Theorem
5. Generalisations of the Central Limit Theorem
Glossary
TEACHING UNIT 5. Hypothesis testing
1. Introduction to statistical hypotheses
2. Hypothesis testing
3. Parametric hypothesis testing
3.1. Hypotheses in parametric tests
3.2. Contrast statistic
3.3. The power of contrast
3.4. Properties of contrast
4. Types of error
5. Non-parametric tests
5.1. Chi-square
Glossary
TEACHING UNIT 6. Linear regression
1. Introduction to regression models
2. Regression models: applicability
3. Variables to be included in the regression model
3.1. Types of variables to be included in the model
4. Building the regression model
4.1. Selection of model variables
4.2. Methods for constructing the regression model
4.3. Deriving and validating the most appropriate model
5. Linear regression model
6. Logistic regression model
7. Confounding factors
8. Interpretation of the results of regression models
Glossary
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