Understanding Statistics: Singular and Plural Sense

Singular Sense of Statistics

• In the singular sense, statistics refers to the study of the collection, analysis, interpretation, presentation, and organization of data.

Plural Sense of Statistics

• In the plural sense, statistics refer to the data itself, i.e., a set of quantitative data that summarizes or describes a phenomenon.

Statistics vs. Probability

• The main difference between statistics and probability is that probability deals with chance events and their likelihood of occurrence, while statistics deals with the analysis and interpretation of data that has already occurred.

Role of a Statistician

• A statistician formats the data to extract meaningful information and draw conclusions.

Relation to Population

• Statistics relates to the entire population of interest by attempting to make inferences about the population based on a sample of data.

Guiding Principles

• A statistician is guided by the likelihood principle in postulating a probabilistic model for the system under investigation.

Focus of Statistics

• In the singular sense, the main focus of statistics is to extract meaningful information from data.
• In the plural sense, the main focus of statistics is to summarize and describe data.

Key Concerns

• The primary concern of statistics is to make inferences about the population, whereas probability focuses on the likelihood of events.
• Descriptive statistics focuses on describing the basic features of the data, while inferential statistics involves making generalizations about the population from a sample.

Descriptive vs. Inferential Statistics

• Descriptive statistics involves summarizing and describing the basic features of the data.
• Inferential statistics enables us to make generalizations about the population based on a sample of data.

Sample Statistic

• A sample statistic describes a characteristic of a sample.

Population Parameter

• A population parameter is a characteristic of the whole population.

Inferential Statistics

• Inferential statistics involves making generalizations about the population based on a sample of data, and attempts to generalize characteristics of the population.