Summary of Statistik: Varianz und Standardabweichung - FernUni Hagen - Psychologie

Main Ideas

• Data Series Introduction
  • Series 1: 10, 20, 30, 40, 50
  • Series 2: 28, 29, 30, 31, 32
• Mean Calculation
  • Series 1 Mean: (10 + 20 + 30 + 40 + 50) / 5 = 30
  • Series 2 Mean: (28 + 29 + 30 + 31 + 32) / 5 = 30
• Understanding Dispersion

  The video emphasizes the need for a measure of Dispersion to understand how much the data points deviate from the mean. It introduces various measures of Dispersion, including the range and Standard Deviation.

• Range Calculation
  • Range for Series 1: 50 - 10 = 40
  • Range for Series 2: 32 - 28 = 4
• Standard Deviation

  Standard Deviation is described as the average distance of data points from the mean. It is calculated by first determining the Variance, which is the average of the squared deviations from the mean.

• Mean Absolute Deviation

  The Mean Absolute Deviation (MAD) is calculated for the first Data Series to illustrate the concept of Dispersion.

  MAD for Series 1 is calculated as:

  • Deviations: |10-30|, |20-30|, |30-30|, |40-30|, |50-30| = 20, 10, 0, 10, 20
  • MAD = (20 + 10 + 0 + 10 + 20) / 5 = 12
• Variance Calculation

  Variance for Series 1:

  • Deviations squared: (-20)², (-10)², 0², 10², 20² = 400, 100, 0, 100, 400
  • Variance = (400 + 100 + 0 + 100 + 400) / 5 = 200

  Standard Deviation for Series 1 = √200 ≈ 14.1

• Calculating for the Second Data Series

  Variance for Series 2:

  • Deviations squared: (28-30)², (29-30)², (30-30)², (31-30)², (32-30)² = 4, 1, 0, 1, 4
  • Variance = (4 + 1 + 0 + 1 + 4) / 5 = 2

  Standard Deviation for Series 2 = √2 ≈ 1.4

• Comparison of Results

  The Standard Deviation of Series 1 (14.1) is significantly higher than that of Series 2 (1.4), indicating greater Dispersion in Series 1.

Methodology

• Calculating Mean: Sum all data points and divide by the number of points.
• Calculating Mean Absolute Deviation: Find deviations from the mean, take absolute values, sum them, and divide by the number of points.
• Calculating Variance: Find deviations from the mean, square them, sum the squares, and divide by the number of points.
• Calculating Standard Deviation: Take the square root of the Variance.

Speakers/Sources

The video is from FernUni Hagen, focusing on Statistics in psychology. The speaker is not explicitly named in the subtitles.

Notable Quotes

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Category

Educational

Video