Fundamentals of Statistical Concepts and Terminology

1. Define Statistical Concepts

Statistics Definition

Statistics is a discipline that uses mathematical tools to organize and summarize a large amount of data obtained from reality, and make inferences about them.

2. Application Areas of Statistics

Statistics can be applied to any realm of reality. Thus, it is used in:

• Physics
• Chemistry
• Biology
• Medicine
• Astronomy
• Psychology
• Sociology
• Linguistics
• Demography, and so on.

3. Defining the Statistical Study Group

The data set which covers a given population is called a statistical study.

4. Population: Demographic vs. Statistical Sense

The difference between the population in the demographic sense and the statistical sense is significant:

• Demographic Sense: A set of individuals (e.g., all residents of a country, all the rats in a city).
• Statistical Sense: A set of data on a certain characteristic or attribute of individuals (e.g., ages of all individuals in a country, the color of all the rats in a city).

Even a statistical population does not have to refer to many individuals. A statistical population may also be the set of scores achieved by an individual throughout their university studies.

5. Procedure for Obtaining Data from the Entire Population

If you want to get data from the entire population, the procedure used is a census.

6. What is the Sample?

A sample is a subset of the population, preferably representative of it.

7. Individual Data vs. Statistics

The difference lies in the scope of the measurement:

• Individual Datum: A datum from a single individual. For example, the age of John.
• Statistic: A fact or measure derived from a sample or population as a whole. For example, the average age of a sample or population of people.

These two measures may not coincide. For instance, John's age might be 37, while the average age of the sample he belongs to is 23 years. Therefore, a statistic says nothing about individuals, as it only describes a sample or population.

8. Statistics vs. Parameters

These terms differentiate between sample and population descriptors:

• Statistics: Descriptors that describe a sample (e.g., the average monthly income of people in a sample).
• Parameters: Descriptors of a population (e.g., the average monthly income of a population).

9. What is Data?

Data is a category assigned to a variable of a unit of analysis.