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.