Measures of Central Tendency

Jun 13, 2024

Review flashcards

Measures of Central Tendency Lecture

Introduction

  • Revisiting the table from a previous session
  • Understanding descriptive statistics
  • Types of variables: Nominal, Ordinal, Interval, and Ratio
  • Organizing individual scores into frequency distributions
  • Calculating percentiles
  • Importance of finding the average or midpoint

Measures of Central Tendency

  • Three types of averages: Mode, Median, Mean
  • Depending on variable type, different measures are used

Variables Recap

  • Categorical (Nominal, Ordinal): Use words for categories
  • Continuous (Interval, Ratio): Use numbers for measurements

Example Variables

  1. Scores (0 - 100): Continuous, Ratio
  2. Favorite Colors: Categorical, Nominal
  3. Age: Continuous, Ratio
  4. Gender: Categorical, Nominal
  5. Income: Continuous, Ratio
  6. Grades (A through F): Categorical, Ordinal
  7. Types of Cars: Categorical, Nominal
  8. Height: Continuous, Ratio
  9. Weight: Continuous, Ratio
  10. Pain Scale (0 - 10): Continuous, Interval

Measures Applicable to Variable Types

  • Nominal: Use Mode
  • Ordinal: Use Median
  • Interval/Ratio:
    • Skewed data: Use Median
    • Normal distribution: Use Mean

Definitions

  • Mode: Most frequently occurring category
    • Example: Scores (2, 3, 7, 7, 8) → Mode = 7
  • Mean: Sum of all scores divided by the number of scores
    • Example: Scores (5, 6, 7, 8, 9) → Mean = 7
  • Median: Middle number in a sorted list
    • Example: Scores (5, 6, 7, 8, 9) → Median = 7
    • For even number of scores: Mean of two middle numbers

Distribution Types

  • Normal Distribution (Bell Curve):
    • Symmetrical with a hump in the middle
    • Mean, Median, and Mode are identical
  • Skewed Distribution:
    • Positive Skew: Hump to the left side, long tail to the right
    • Negative Skew: Hump to the right side, long tail to the left

Distribution Examples

  • Positive Skew:
    • Mode: At the hump
    • Mean: Pulled towards the larger numbers (long tail)
    • Median: Between Mode and Mean
  • Negative Skew:
    • Mode: At the hump
    • Mean: Pulled towards smaller numbers (long tail)
    • Median: Between Mode and Mean

Determining Skew

  • Positively Skewed: Mean > Median
  • Negatively Skewed: Mean < Median

Application

  • Nominal & Ordinal Data: Report Mode
  • Interval & Ratio Data: Check distribution
    • Skewed data: Report Median
    • Normal distribution: Report Mean