data management

Overview of Statistics in Mathematics

Introduction to Statistics

  • Statistics: The art and science of learning from data.

  • Involves collection, presentation, analysis, and interpretation of variable data.

  • Defined by W.A. Wallis as methods for wise decision-making amid uncertainty.

Importance of Practical Engagement

  • Engaging with statistical procedures by hand enhances understanding.

Applications of Statistics

Practical Applications

  1. Determine the income distribution of families.

  2. Compare effectiveness of therapy techniques.

  3. Predict daily temperatures.

  4. Evaluate student performance.

Role in Scientific Process

  • Statistics tests hypotheses via:

    • Proposing a question/hypothesis.

    • Collecting data through studies/experiments.

    • Analyzing results to validate or refute hypotheses.

Aims of Statistics

Major Aims

  1. Uncover structure in data.

  2. Explain variations in data.

Types of Statistics

Descriptive Statistics

  • Methods for collecting, organizing, and analyzing data without making conclusions about larger sets.

  • Example: Analyzing COVID-19 mortality trends in the Philippines.

Inferential Statistics

  • Methods for making predictions about a larger population based on sample data.

  • Example: Evaluating vaccine efficacy through sample data.

Basic Statistical Concepts

Key Terms

  • Universe/Population: Entire set of individuals or entities studied. Example: Basic education teachers in a stress study.

  • Variable: Characteristic or attribute that varies among subjects. Examples include heart rate, test score, and favorite color.

Types of Data

Qualitative Data (Categorical)

  • Data categorized based on characteristics. Example: Grouping by marital status, socioeconomic status.

Quantitative Data

  • Data that can be counted or measured (Discrete or Continuous).

  • Examples: Number of students, weight of respondents.

Classification of Data

  • By Time:

    • Cross-sectional

    • Time series

    • Longitudinal

  • By Source:

    • Primary data

    • Secondary data

Statistical Population and Sample

  • Statistical Population: Collection of all cases in statistical study; described by parameters.

  • Sample: Subset of the population; described by statistics.

Statistical Measures and Symbols

  • Mean (µ or x̄), Standard Deviation (σ or s), Variance (σ² or s²), Pearson Correlation Coefficient (ρ or r), Number of Cases (N or n).

Levels of Measurement

Nominal Scale

  • Categorization without a specified order. Examples: Gender, race.

Ordinal Scale

  • Indicates rank order without equal intervals. Examples: Socioeconomic status, class standings.

Interval Scale

  • Indicates quantities with equal intervals but no true zero. Examples: Temperature, exam scores.

Ratio Scale

  • Reflects true quantities with a clear zero point. Examples: Height, weight, income.