Statistics 3rd Quarter Quiz

Statistics 3rd Quarter

• This quarter covers fundamental statistical concepts, data collection methods, data sources, types of data, uses of statistics in various fields, data presentation methods, and sampling techniques.

Basic Concepts on Statistics

• Statistics is the scientific study of collecting, organizing, presenting, analyzing, and interpreting data to gain meaningful insights.

Etymology of Statistics

• The word "statistics" originates from the Latin word "statisticus," meaning "of the state."
• It's derived from the Italian word "statisticum collegium," signifying "council of state."
• The German term "statistik" was introduced by Gottfried Achenwall, representing the science of state.

Data Collection

• Data collection involves gathering information or data.
• This process is crucial for various research applications.
• Data organization and presentation summarize collected data in text (written), graphical, or tabular (chart-based) forms.

Collection, Organization, Analysis and Interpretation Process

• Collection: Gathering information (data).
• Organization/Presentation: Summarizing the data in various formats (text, tables, charts).
• Analysis: Inspecting the data using statistical methods.
• Interpretation: Drawing conclusions from the analyzed data.

Data Sources

• Population: The complete set of all objects, persons, places, or events under study with a certain characteristic. Denoted by 'N'.
• Sample: A subset of a population, collected through sampling procedures (commonly random selection). Denoted by 'n'.

Population and Sample

• Parameter: A numerical or nominal characteristic of a population. Measured from the entire population.
• Statistic: An estimate of a population parameter, measured from a sample.

Types of Data

• Qualitative (Categorical): Data grouped into categories;
  • Nominal: Categories without inherent order (e.g., gender, colors).
  • Ordinal: Categories with a natural order (e.g., rankings, educational levels).
• Quantitative (Numerical): Data represented by numbers;
  • Discrete: Counted, not measured (e.g., number of siblings).
  • Continuous: Measured (e.g., height, temperature).
    • Interval: Difference between values is meaningful, but no true zero (e.g., temperature in Celsius).
    • Ratio: Difference between values is meaningful, and there's a true zero (e.g., Height, weight).

Uses of Statistics

• Education: Assessing student performance and teaching/learning processes to foster equality.
• Psychology: Determining attitudes, causes of misbehavior, and impacts.
• Business and Economics: Analyzing data related to sales, output, prices, revenues, and costs.
• Research and Experimentation: Validating claims or inferences about groups of people or events.
• Medicine: Collecting patient and disease data for treatment decisions.

Data Collection Methods

• Interview: Direct interaction with individuals for gathering data.
• Questionnaire: Standardized list of questions distributed to subjects.
• Historical Records: Existing documents or data for analysis.
• Observations: Recording events as they occur.
• Discussions/Focus Groups: Gathering input through interactive sessions.
• Experiments/Case Studies: Conducting experiments or analyzing specific cases.

Sampling Techniques

• Probability Sampling: Each population member has an equal chance of being selected.

  • Random Sampling: Selecting subjects randomly using random numbers.
  • Systematic Sampling: Selecting every 'k'th member after a random starting point.
  • Stratified Random Sampling: Dividing the population into subgroups and sampling randomly from each.
  • Cluster Sampling: Randomly selecting groups or clusters from the population then sampling from.
  • Multi-stage Sampling: Combining several probability sampling techniques for very large populations.

• Non-probability Sampling: Does not guarantee equal selection chance.

  • Convenience Sampling: Selection based on convenience or accessibility.
  • Quota Sampling: Selecting subjects based on pre-defined proportions of subgroups.
  • Purposive Sampling: Conscious selection of specific individuals based on criteria.

Frequency Distribution Table

• A tabular representation of observations, sorted into classes showing their frequency.
  • Ungrouped Data: Raw data arranged systematically.
  • Grouped Data: Raw data categorized into groups with specified intervals.
    • Components include: Lower and Upper Class Limits, Class boundaries, Class Width(size), Cumulative frequency,

Data Presentation

• Textual: Describing data using words.
• Tabular: Presenting data in tables.
• Graphical: Visualizing data using charts (bar charts, histograms, pie charts, ogives, frequency polygons).