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Practical Session: Case Studies and Probabilities

May 21, 2024

Practical Session: Case Studies and Probabilities 📊

Introduction

  • Topic: Focus on Case Studies 1, 2, and 3; Binomial Distribution will be covered later.
  • Next Steps:
    • This week: Case Studies 1-3
    • Week after next: Binomial Distribution integrated with lectures
    • Q&A sessions for all practicals (Case Studies 1-3) this week

Practical 3 Overview

  • Objectives: Understand the use of sample data and population data in case studies.
    • Specific note: For some case studies, consider the data as population data (census).
  • Submission: Available on Saturday morning.

Functions Needed

  • Excel Functions: SUMPRODUCT, COUNT, COUNTIF, and SQRT
  • Binomial Distribution (BINOM_DIST): To be covered in future sessions.

Practical 3 Content

  • Probabilities Using Cross Tabulations: Follow-up from Practical 1
  • Empirical Probability Distributions: Introduction and observation in Excel
    • Key terms: Empirical (Observed) probability distributions
    • Expected Value and Variance
  • Counting Techniques: To be covered today
  • Binomial Probability: To be integrated with future sessions

Case Study 1: Empirical Probability Distributions

Concepts to Understand

  • Population Data Assumption: Important for calculating expected values and variances.
  • Classical, Relative Frequency, and Subjective Methods:
    • Classical: Assumes each outcome equally likely
    • Relative Frequency: Based on observed frequencies
    • Subjective: Based on educated guesses

Steps in Excel

  1. Calculate Frequency Distribution:
    • Use PivotTable to create distribution (count occurrences)
    • Be sure to use COUNT instead of SUM
    • Filter data for relevant ranges (e.g., up to 10 trips)
  2. Calculate Probabilities:
    • Convert frequencies to probabilities by dividing by total observations
    • Use SUMPRODUCT for efficient calculations

Calculations

  • Expected Value (Mean):
    • Formula: SumProduct(X values, Probabilities)
    • Represents the average value of X
  • Variance:
    • Formula: SumProduct((X - Mean)^2, Probabilities)
    • Measures the spread of data around the mean
  • Standard Deviation:
    • Calculate as SQRT(Variance)

Case Study 2: Joint, Marginal, and Conditional Probabilities

Overview

  • Cross Tabulation: Use two variables to calculate joint, marginal, and conditional probabilities
  • Steps:
  1. Insert PivotTable for cross tabulation
  2. Use HomePhone and TypeOfDwelling variables
  3. Change to show values as percentages of grand total

Probability Types

  • Joint Probabilities: Deals with two variables
  • Marginal Probabilities: In the margins, dealing with single variables
  • Conditional Probabilities: Based on given conditions
    • Use Percentage of Row Total or Percentage of Column Total

Case Study 3: Counting Techniques

Concepts

  • Factorials, Combinations, and Permutations:
    • FACT: Factorial
    • COMBIN: Combination
    • PERMUT: Permutation

Steps

  1. Identify Population Size and Sample Size
  2. Determine Calculation Type
    • Use appropriate Excel function based on the requirement (Factorial, Combination, Permutation)

Conclusion

  • Binomial Probabilities: To be covered in future sessions
  • Q&A Sessions: Available for all practicals, including review of previous practicals
  • Important Note: Ensure accurate application of theoretical concepts to practical problems

Enjoy your week and good luck with the practicals!

Full transcript