Statistics Fundamentals

The Language of Statistics

• An experiment or investigation is a process of observation or measurement.
• Elements are people or objects about which information is collected.
• A population is a complete collection of elements; it can be finite (countable number of items) or infinite (unlimited number of items).
• A study of the entire population is known as a census.
• A parameter is a numerical measure that describes a population, usually indicated by a Greek alphabet letter (e.g., μ, σ, π).

Samples and Statistics

• A sample is a portion of data drawn from a population, and must be representative of the population.
• A statistic is a numerical measure that describes a sample, usually indicated by a Roman alphabet letter (e.g., x̅, s, p).

Variables

• A variable is a characteristic of interest about each element of a population or sample, which varies from element to element.
• Variables can be classified as:
  • Qualitative or categorical (non-numerical, e.g., marital status, type of job, gender) and may be coded to appear quantitative but lack numerical meaning.
  • Quantitative (numerical measurements, e.g., height, weight, age, temperature of water).

Activity 1.2

• Question to be answered: What is the proportion of students who favour a change in admission requirements?
• Variable of interest: Attitude towards the proposed change in admission requirements.
• Classification of variable: Qualitative or categorical.
• Population of interest: All 10,000 students at the university.
• Sample: 200 students interviewed.
• Sample statistic: 32% of students are in favour of the change.
• Population parameter: Proportion of all students who are in favour of the change.

Role of the Computer in Statistics

• The Internet provides access to data across continents at low costs.
• Computers are useful for:
  • Large volume of input
  • Repetition of projects
  • Faster processing
  • Greater accuracy
  • Processing complexities that require electronic help
• Computers help in developing ideas about organizing information using a "try and refine" approach.

Outcomes

• Recognize the role of statistics in life
• Understand the language of statistics
• Select suitable measuring scales for different types of data
• Understand the role of computers in statistics

Problem-Solving Steps

• Identify the problem
• Collect the information (data): how to measure it, what is the appropriate data source, use population or sample, and which sampling method?
• Organize and summarize the information: tables, graphs, numerical summaries
• Interpret results: draw conclusions, make recommendations, assess the risk of an incorrect decision