A simple noncalculus proof that the median minimizes the sum of the absolute deviations

1. Does the median minimizes the sum of absolute deviations?
2. What is the value that minimizes the sum of all absolute deviations from it?
3. How do you minimize mean absolute error?
4. What is the sum of deviation about median?

Does the median minimizes the sum of absolute deviations?

It is widely known among statisticians that the median minimizes the sum of the absolute deviation about any point for a set of x's, xl, x2, x3, . . . , x,.

What is the value that minimizes the sum of all absolute deviations from it?

The Median minimizes the sum of absolute deviations. The Mean minimizes the sum of squared deviations (sum of squared errors). The Midpoint minimizes the biggest deviation.

How do you minimize mean absolute error?

the mean absolute error of the prediction, is minimized when a is any median of the distribution of X.

What is the sum of deviation about median?

Where a = First term, n = nth term, d = common difference. ∴ The sum of the deviations measured from the median is 0.