How do I show that the sample median minimizes the sum of absolute deviations?
31910
Mean and Median properties
70886
Hypothesis testing with the geometric distribution for dummies
120182
For what (symmetric) distributions is sample mean a more efficient estimator than sample median?
41930
Mean of $ \sum (X_i - \bar{X})^2$
84694
Deriving ordered statistics minimum cdf
91446
Average arc length of a uniformly distributed points
24602
Minimize the standard deviation in list of numbers by subtracting from each value
95719
Drawing a triangle from medians
78733
Finding the density for $\min\{X, Y\}$
133753
When does the amount of skew or prevalence of outliers make the median preferable to the mean?
10079
Standard error of the median
121692
Showing that estimator is consistent
116689
Joint distribution of range $(R=X_n-X_1)$ and mid-range $(V=\frac{1}{2}(X_1+X_n)$order statistics
127861
Finding Local Minima / Maxima in Noisy Data
44278
$R^2$ for least absolute deviation regression
109310
Understanding “the mean minimizes the mean squared error”
34076
Can we detect the existence of outliers using mean and median?