University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

45

Pages:

2
Author:

Niklas

Lecture 1: Statistics Statistics is the science of collecting data and extracting information to help understand phenomena. When analyzing a phenomenon, the first step is to ask a question about it. Statistics helps collect and analyze data to answer that question. First Data Application of Statistics Micro: Sale forecast Customer profiling Credit Finance Insurance Macro: Macroeconomic forecast Estimate of macroeconomic aggregates Empirical verification of economic relations Example: The Gross Domestic Product (GDP) growth rate is inversely proportional to the unemployment growth rate: A(GDP) = X + BA(Unempl) The theoretical relationship can be compared with empirical observations to confirm the theory and give values to A and B for making predictions. The Steps of a Statistics Analysis Formulate a question: Translate a cognitive need into a question that can be answered. Identifying or collecting data: Broad topic known as experimental design and sampling. Organize and take a look at the data: Synthesize the extracted data and/or represent it graphically. Modeling: Formulate a probabilistic model that explains the observed data based on assumptions made about the phenomenon. The model can be used to confirm or deny hypotheses about the phenomenon or make predictions for future instances. Population and Statistics Unit Population: The entire group, a complete set of units. Finite: It is possible to count its individuals. Infinite: Cannot be calculated easily, they are unlimited in size. Statistics unit: Each component of the population. Variables: Any characteristics, number, or quantity that can be measured or counted. Lecture 1: Statistics (Continued) Sampling Procedure When we cannot observe the entire population, we use a sampling procedure. We observe just a part of the population, the sample, and we generalize to the whole population what was observed on the sample. Sample: A subset of the population. Representative sample: A sample that represents the whole population. Exploratory-descriptive analysis: When you test if the sample is conclusive. Statistical Data A statistical data is the result of the survey of some characteristic on a statistical unit belonging to a population. Statistical unit: Individual component of the population. Variable: Elementary aspect surveyed on the statistical units of the population. Modalities/Categories of a Variable The different ways in which the variable presents itself. Expressed in a numerical form: Numerical: Continuous: The set of modalities is a range, limited or unlimited. Discrete: The set of modalities is finite or countable. Expressed in a verbal form: Categorical: Ordinal: Modalities imply an order. Nominal: Modalities do not imply an order. Examples: What's the type of variable of "city of residence"? What's the type of variable of "education level"? How many hours did you sleep last night? Variables are typically listed in the columns of a data set, with the rows referring to individual observations.