I am trying to solve this question, but have no idea how one can prove it:  Let $m$ be the median of the array $A$ with $n$ real numbers. Show that $$\sum_{i=1}^{n}\bigg|A[i]-x\bigg|$$ is minimal for $x = m$.  Thank you for your help!
Suppose we have a set $S$ of real numbers. Show that   $$\sum_{s\in S}|s-x| $$   is minimal if $x$ is equal to the median.    This is a sample exam question of one of the exams that I need to take and I don't know how to proceed.
What's going on here? I've installed the  on Ubuntu 17.10. Everything was cool, and as I was trying to hone and tweak the look of my desktop, at some point the shortcuts bar (dock?) on the left is duplicated.  (Click image to enlarge) The default, which normally disappears with Dash to Dock, is there underneath the one that usually shows up when I install Dash to Dock. Why? I've tried to go through the options for Dash to Dock, the GNOME Tweak Tool, and the regular Ubuntu settings, but I can't figure it out. Table of contents numbering is strange Another word for a troll not on the internet The definition of an internet troll:     In Internet slang, a troll (/ˈtroʊl/, /ˈtrɒl/) is a person who sows   discord on the Internet by starting arguments or upsetting people,   by posting inflammatory,[2] extraneous, or off-topic messages in an   online community (such as a forum, chat room, or blog), either   accidentally[3][4] or with the deliberate intent of provoking readers   into an emotional response[5] or of otherwise disrupting normal   on-topic discussion.[6]      This sense of the word troll and its associated verb trolling are   associated with Internet discourse, but have been used more widely.   Media attention in recent years has equated trolling with online   harassment. For example, mass media has used troll to describe "a   person who defaces Internet tribute sites with the aim of causing   grief to families."[7][8]     What is the equivalent for a person who does this type of thing in real life (non-cyber) troll? Refresh thumbnails in nautilus How does one refresh thumbnails in nautilus? In my videos folder I have some MKVs and only half of them have the movie border and a excerpt from the movie and the others (also MKVs encoded in the same way) just have the ordinary film icon.  (F5 doesnt do it.) Should I flag/down-vote "Draft Answers"? Is there any significant difference between Nikon and Canon? UV mapping a straight image around a ring shaped flat mesh Is it possible to mapping a image around a ring shaped mesh? I would imagine there should be a way to curve/distort the image around the mesh. If not, how can I straighten out the mesh easily instead to fit the image? How do I change the MAC address of my network card? I have a local network in a Windows system where the Admin gives permission to the PCs by their MAC address. But he is on vacations and I have a new PC.  How can I change the MAC address of my new PC to have the same MAC address as the old one?  I know this can be used for spoofing the address, but this is local, so I don't think I will have a problem. Can I use a EF lens with a EF-S camera? Special event cards and timing How does Python evaluate the expression 1+++2?  How many ever + I put in between, it is printing 3 as the answer. Please can anyone explain this behavior  And for 1--2 it is printing 3 and for 1---2 it is printing -1 How to install networkx python in QGIS? How to install and how to compile networkx python on QGIS?  I always get an error that no module named networkx in the console of QGIS I copied the file networkx in C:\Program Files\Quantum GIS Lisboa\apps\Python27\Lib\site-packages and there are not change. How to get/suppress french spacing before punctuation in `\href` Attention I have already a possible answer and will add it soon. I thought it would be useful to have a solution about it on the site. (Other answers are naturally welcome too).  Question How to activate or suppress the french spacing before some punctuations like a colon in the text argument of \href locally (for one specific \href) and globally? Switching the language is not an answer!  Minimal examples for tests (the argument of \href should normally be a valid url, so it is a bit unfair to add an example without a colon in the link):  pdflatex  With pdflatex it depends on the link how the argument of \href is printed:  \documentclass{article} \usepackage[french]{babel}  \usepackage{hyperref}  \begin{document} With pdflatex no french spacing in links with colons:   \href{link}{a:b}  \href{link:colon}{a:b}  \end{document}     lualatex  With lualatex the spaces are always there:  \documentclass{article} \usepackage[french]{babel}  \usepackage{hyperref}  \begin{document} With lualatex always spaces:  \href{link}{a:b}  \href{link:colon}{a:b}  \end{document} How does the T-1000 see? In Terminator 2: Judgement Day, how does the T-1000 sense things? It's made of mimetic poly alloy; however, does it have a retinal scan camera like the T-X or T-800, or is just molecules that allow it to see what it does? In other words: let's say it is made out of nanobots. Would a group of these nanobots provide the capability of sight? Kind of like humans with cells that  make up the brain? I have always wondered whether James Cameron explained this on a special edition or if the topic was left up for insight from Terminator fans. From what I get from the whole mimetic poly alloy and some of the extra scenes, it seems to feel its way out to get information. Of course, it's very much not blind! Thoughts? Big floor symbols When I write  \lfloor\dfrac{1}{2}\rfloor   the floors come out too short to cover the fraction. How can I lengthen the floor symbols? How to compare Unicode strings in Javascript? The difference between GPU and CPU I know what a CPU is(I think). It's the thing who's speed is measured in GigaHertz(these days).  However, you hear a lot about a GPU, and letting the GPU take over, not letting the CPU but the GPU do it, GPU-based rendering, etc...  What is this GPU anyway? How can I access it and use it to my advantage? What am I missing out on here? Can the system leave a deletion reason when it deletes a question? What are the differences between a multidimensional array and an array of arrays in C#? What are the differences between multidimensional arrays double[,] and array-of-arrays double[][] in C#?  If there is a difference, what is the best use for each one? Help Me Understand My Bicycle's Gears