STA 111: Descriptive Statistics

Study Notes

Descriptive statistics is a branch of science that deals with the collection, presentation, analysis, and interpretation of data.
It is the scientific process for making valid decisions in the face of uncertainty.
It is also referred to as the "Science of processing data".

There are two broad areas of Statistics study:
- Descriptive Statistics: concerned with methods for presenting and summarizing sample data.
- Inferential Statistics: concerned with methods of using the summary information and findings from a sample to draw conclusions about a population.

Statistics plays a key role in various fields, including:
- State economy: provides summary measures of economic variables and acts as a management tool.
- Health, Energy, Environmental Studies, Government, Telecommunication, Transportation, etc.: helps to release the right information needed in policy formation and decision making.
- Risk assessment and dynamics: increasingly used in risk assessment and dynamics.
- Control Theory: essential for every scientist to master these tools.

Probability and statistics are used throughout engineering to analyze data.
Statistical methods are used in developing and implementing data-driven technologies.
Statistics methods provide frameworks that help in identifying trends and patterns in data, useful in business decisions.
Data science techniques like machine learning and Artificial intelligence rely on statistical tools for analyzing and implementing big data.

Observations: the units on which we measure data, such as persons, cars, animals, or plants.
Population: the collection of all units.
Sample: a selection of observations from a population.
Variable: a particular feature of observations that can be collected in a statistical variable X.

Qualitative variables: take values that cannot be ordered in a logical or natural way, such as the color of the eye or the name of a political party.
Quantitative variables: represent measurable quantities, such as the size of shoes or the price of houses.
Discrete variables: can only take a finite number of values, such as the size of shoes or the number of semesters studied.
Continuous variables: can take an infinite number of values, such as the time it takes to travel to university or the length of an antelope.

Nominal scale: the values of a nominal variable cannot be ordered, such as the gender of a person (male–female) or the status of an application (pending–not pending).
Ordinal scale: the values of an ordinal variable can be ordered, but the differences between these values cannot be interpreted in a meaningful way, such as the education level (none–primary education–secondary education–university degree).
Continuous scale: the values of a continuous variable can be ordered, and the differences between these values can be interpreted in a meaningful way, such as the height of a person.
Interval scale: only differences between values, but not ratios, can be interpreted, such as temperature (measured in °C).
Ratio scale: both differences and ratios can be interpreted, such as speed.
Absolute scale: the same as the ratio scale, with the exception that the values are measured in "natural" units, such as the number of semesters studied.