STA 111: Descriptive Statistics

Descriptive Statistics

• 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".

Areas of Statistical Study

• 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.

Role of Statistics

• 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.

Statistics in Software Engineering and Computer Science

• 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.

Basic Concepts in Statistics

• 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.

Variables

• 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.

Scales

• 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.