Pre-sessionals - Stats 1

Introduction to Basic Statistics

• Introduction to Statistics

  • What is Statistics and its Importance
    • Define statistics as the study of data collection, analysis, and interpretation.
    • Explain the importance of statistics in decision-making and research.
    • Example: Discuss how statistics are used in medical research.
  • Descriptive vs. Inferential Statistics
    • Differentiate between descriptive and inferential statistics.
    • Emphasize the role of each in understanding and drawing conclusions from data.
    • Exercise: Provide scenarios and determine whether descriptive or inferential statistics would be used.
  • Types of Data: Categorical and Numerical
    • Explain the distinction between categorical and numerical data.
    • Provide examples of each type of data.
    • Exercise: Classify given data sets as categorical or numerical.

• Measures of Central Tendency

  • Mean, Median, and Mode
    • Define and explain the concepts of mean, median, and mode.
    • Illustrate how to calculate each measure.
    • Example: Calculate mean, median, and mode for a set of exam scores.
    • Exercise: Compute mean, median, and mode for different data sets.
  • Calculating and Interpreting Each Measure
    • Discuss the interpretation of mean, median, and mode in terms of centrality.
    • Highlight scenarios where each measure is useful.
    • Exercise: Analyze the implications of outliers on measures of central tendency.
  • Real-World Examples
    • Provide real-world examples where mean, median, and mode are applied.
    • Discuss their relevance in various contexts, such as finance or education.
    • Exercise: Analyze a dataset from a real-world scenario and calculate central tendency measures.

• Measures of Dispersion

  • Range, Variance, and Standard Deviation
    • Define and explain the concepts of range, variance, and standard deviation.
    • Demonstrate how to calculate each measure.
    • Example: Calculate the range, variance, and standard deviation for a data set.
    • Exercise: Compute range, variance, and standard deviation for different datasets.
  • Interpreting Variability
    • Discuss the importance of measures of dispersion in understanding data spread.
    • Explain how variability affects the interpretation of central tendency measures.
    • Exercise: Compare and contrast datasets with different measures of dispersion.
  • Variance and Standard Deviation for Populations vs. Samples
    • Explain the difference between calculating variance and standard deviation for populations and samples.
    • Discuss when to use the population formula versus the sample formula.
    • Example: Calculate the population and sample variance and standard deviation for a dataset.

• Quantiles and Percentiles

  • Definition of Quantiles and Percentiles
    • Define quantiles and percentiles as measures of position in a dataset.
    • Explain how they divide data into equal parts.
    • Exercise: Calculate the quartiles and percentiles for a dataset.
  • Calculation and Interpretation
    • Discuss how to calculate quantiles and percentiles using order statistics.
    • Interpret the meaning of specific quantiles and percentiles.
    • Example: Calculate the interquartile range and 75th percentile for a dataset.
    • Exercise: Calculate and interpret quantiles and percentiles for various datasets.
  • Box Plots and Their Use in Visualizing Quantiles
    • Explain how box plots represent the five-number summary and outliers.
    • Discuss the components of a box plot (whiskers, box, median, outliers).
    • Example: Create a box plot for a dataset and analyze its features.
    • Exercise: Construct box plots for given datasets and identify characteristics.

• Conclusion and Recap

  • Summarize the key concepts covered in the lecture.

• Q&A Session

• Reference: Statistics for Business, 2nd edition. R. A. Stine, D. Foster