Section 14 Measures of Spread
Estimator of dispersion of the data
14.3 Mean Absolute Deviation (MAD)
Mean absolute deviation around the mean or average absolute deviation
\[ \Huge MAD = \frac{1}{n}\sum\limits_{i=1}^{n} |(x_i-\bar{x})| \]
- Alternative forms: - Mean absolute deviation around the median - Median absolute deviation around the mean - Median absolute deviation around the median
14.4 Variance
\[ \large Var(x) = s_x^2 = \frac{1}{n}[(x_1-\bar{x})^2 + (x_2-\bar{x})^2 + ... + (x_n-\bar{x})^2] \]
\[ \Huge Var(x) = s_x^2 = \frac{1}{n}\sum\limits_{i=1}^{n} (x_i-\bar{x})^2 \]
14.5 Standard Deviation
\[ \Huge s_x = \sqrt{s_x^2} \]
Two Definitions of Variance
- Population Variance
- Sample Variance
Population Variance
\[ \Huge Var(x) = s_x^2 = \frac{1}{n}\sum\limits_{i=1}^{n} (x_i-\bar{x})^2 \]
Sample Variance
\[ \Huge Var(x) = s_x^2 = \frac{1}{n-1}\sum\limits_{i=1}^{n} (x_i-\bar{x})^2 \]
- Centering and Scaling of data - Mean - Variance - Standard Deviation