Problem from **"Competitive Programmer’s Handbook"** by Antti Laaksonen, **Page 61**.↵
↵
The problem is to find x to **minimum** the sum of the equation below:↵
↵
↵
↵
[Image](https://pasteboard.co/JknMyWb.png)↵
↵
I thought the answer will be the **mean** on the number because if we plot the in a 1D number line, the mean will be somewhere middle of them, so the absolute difference of distance between each number and the mean can be minimized.↵
↵
The book says it is the **median**.↵
↵
**Example [1, 2, 2, 6, 9]** ↵
↵
The **mean** will be **19 / 5 = 3.8.** The absolute difference is **13.8.**↵
↵
The **median** is **2** an the absolute difference is **12.** ↵
↵
I know that this is the **absolute sum** not the just the sum. But the median is only limited to the element of the array. Why x should be the **median** instead of the **mean**? Can this be mathematically proved?
↵
The problem is to find x to **minimum** the sum of the equation below:↵
↵
↵
↵
[Image](https://pasteboard.co/JknMyWb.png)↵
↵
I thought the answer will be the **mean** on the number because if we plot the in a 1D number line, the mean will be somewhere middle of them, so the absolute difference of distance between each number and the mean can be minimized.↵
↵
The book says it is the **median**.↵
↵
**Example [1, 2, 2, 6, 9]** ↵
↵
The **mean** will be **19 / 5 = 3.8.** The absolute difference is **13.8.**↵
↵
The **median** is **2** an the absolute difference is **12.** ↵
↵
I know that this is the **absolute sum** not the just the sum. But the median is only limited to the element of the array. Why x should be the **median** instead of the **mean**? Can this be mathematically proved?
