Standard Error vs. Standard Deviation of Sample Mean I'm having difficulty figuring out the difference between (typically referred to as S.E):  A. The Standard Error  And  B. The Standard Deviation of the Sample Mean (typically referred to as s)  Are they the same thing?  OR   S.E is the standard deviation of the the mean of the sampling distribution similar formula as the standard deviation except you use n-1 instead of n in the denominator s is the standard deviation of a single random sample -- same formula as the standard deviation
Difference between standard error and standard deviation I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error?
Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$ Here is an exercise, on analysis which i am stuck.    How do I prove that if $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$, then the sequence $\{F_{n}(x)\}$ is boundedly convergent on $\mathbb{R}$? Why is the Yang-Mills gauge group assumed compact and semi-simple? What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories?  I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even from a computational perspective. really given these assumptions much thought. What is a general rule for use of auxiliary verbs in sentence? Should we duplicate it or not? For instance,     It is available for every item and (is) used with . . . How to configure logback to skip logging messages from org.package.* with all levels below WARN? What does Minecraft's scary music mean? Apparently it means there is a dungeon around but I can never find any?  If it does mean dungeons how far away will it trigger? C++11 does not deduce type when std::function or lambda functions are involved Voldemort was said to be very interested in the four founders of Hogwarts. He created a Horcrux from the Ravenclaw diadem, the Hufflepuff cup, and the Slytherin locket. Did he try to find a Gryffindor relic to complete the set, or did he not bother?   I can't see him giving up on such a task, but maybe there was insufficient time.  Gryffindor's sword was hiding 'inside' the Sorting Hat, but a famous family usually has some other heirlooms too.  If there are no canon answers I'd be interested in your own speculation! 100% Delete U2 from iPhone? I've looked up many ways on how to deal with the U2 songs on my phone, but they will not go away what ever I try.  The most common solution for this problem is to "Show all" music, go to the Music, click the iCloud download button to download it and then turn off "Show all" button again. Generally, this would work but in my situation, it says I haven't purchased the song and I can't download the song again. The song still plays when I click on it, but I can't swipe left to delete and I can't hide it. And yes, I am signed into iTunes. And no, it is not under my purchased section.  Is there any other way to rid of this song?   EDIT:  I'm running iOS7.1.2 on a iPhone5c And the song(s) aren't in my iTunes. It says I have zero items in my iTunes library and it isn't under my purchased songs. The song is only on my iPhone, and I can't redownload it (to delete it again) because then I'd have to purchase the song again.  Thanks. As shown in various episodes ("Mirror, Mirror," "Phantasms," etc.), other universes exist, oftentimes containing the same characters, albeit in different situations than in the prime universe. I'm curious, though, whether individuals that apparently exist outside of the multiverse, such as members of the Q, would not be duplicated elsewhere. It seems reasonable to me, but I'm not sure. Can I use two different cards with the same name in Commander? How is the popularity of "recent tags" calculated? How are these calculated? I see them going up and down all the time, and there are obviously way more than 48 questions about C# so how are these calculated? Live in Florida & work remote for a New York company. Do I owe NY state income tax? I have been down in Florida for the past 3 1/2 years and continue to pay New York state taxes out of the money I earn for a company I work remote for that is in New York.  Should I be paying New York state taxes on this income?  Or do I not need to pay New York state tax because I live in Florida?  Our NY accountant says I need to continue to pay since company is out of NY, however others say I don't need to pay.  Pls advise which is correct. Thank you. How can I add an item to the 'new' context menu? When I right click anywhere I get an option to add a new file with a specified extension. I would like to add some custom files into this menu, so I can right click and create a new PHP file for instance.  How can I do this? K-means is a widely used method in cluster analysis. In my understanding, this method does NOT require ANY assumptions, i.e., give me a dataset and a pre-specified number of clusters, k, and I just apply this algorithm which minimizes the sum of squared errors (SSE), the within cluster squared error.  So k-means is essentially an optimization problem.  I read some material about the drawbacks of k-means.  Most of them say that:   k-means assumes the variance of the distribution of each attribute (variable) is spherical;  all variables have the same variance; the prior probability for all k clusters is the same, i.e., each cluster has roughly equal number of observations;   If any one of these 3 assumptions are violated, then k-means will fail.  I could not understand the logic behind this statement. I think the k-means method makes essentially no assumptions, it just minimizes the SSE, so I cannot see the link between minimizing the SSE and those 3 "assumptions". Does installing and using Wine open up your Linux platform to Windows viruses? Just wondering if installing Wine might open up a fairly solid Linux desktop to the world of Windows viruses.  Any confirmed reports about that?  Would you then install a Windows antivirus product under Wine? Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$ Why does the natural ring homomorphism induce a surjective group homomorphism of units? I'm trying an old problem here:   Suppose $n\mid m$, and I have a natural ring homomorphism $\varphi\colon \mathbb{Z}/m\mathbb{Z}\to\mathbb{Z}/n\mathbb{Z}$ defined by $\varphi(j)=j\mod{n}$. I can verify that this is a ring homomorphism, but why does it induce a surjective group homomorphism on the unit groups $(\mathbb{Z}/m\mathbb{Z})^\times\to(\mathbb{Z}/n\mathbb{Z})^\times$?  My question in particular is why is it surjective? I take $k\in(\mathbb{Z}/n\mathbb{Z})^\times$. Then there exist integers $s,t$ such that $sn+tk=1$. Since $n\mid m$, I can also write $m=na$. So multiplying through I get $sm+tka=a$. I'm lost here. How can I find a unit in $(\mathbb{Z}/m\mathbb{Z})^\times$ which maps to $k$ to show surjectivity? How do I view 'git diff' output with my preferred diff tool/ viewer? When I type git diff, I want to view the output with my visual diff tool of choice (SourceGear "diffmerge" on Windows). How do I configure git to do this? ffmpeg synchonization of libfdk_aac (or libfacc) and libx264 How to synchronize libfdk_aac and libx264 streams?  ffmpeg -i pipe_libfdk_aac.fifo -i pipe_libx264.fifo -c copy -f flv flv_stream_pipe_or_rtmp.output   I'm always receiving the same asych in all cases: saving file on file system, rtmp-using or raw pipe out. Is it possible to syncronize them?   ffmpeg version N-66924-gaba61b2 Copyright (c) 2000-2014 the FFmpeg developers built on Jan 15 2015 12:50:29 with gcc 4.6 (GCC) 20120106 (prerelease) configuration: --arch=arm --cpu=cortex-a8 --target-os=linux --enable-runtime-cpudetect --prefix=/data/data/info.guardianproject.ffmpeg/app_opt --enable-pic --disable-shared --enable-static --cross-prefix=/home/qwerty/work/android-ndk-r10b86/android-ndk-r10b/toolchains/arm-linux-androideabi-4.6/prebuilt/linux-x86/bin/arm-linux-androideabi- --sysroot=/home/qwerty/work/android-ndk-r10b86/android-ndk-r10b/platforms/android-3/arch-arm --extra-cflags='-I/home/qwerty/x264 -I/home/qwerty/ffmpeg_build/mp3/build/include -I/home/qwerty/faac/output/include -I/home/qwerty/ffmpeg_sources/fdk-aac/build/include -I/usr/local/include/ -mfloat-abi=softfp -mfpu=neon' --extra-ldflags='-L/home/qwerty/x264 -L/home/qwerty/ffmpeg_build/mp3/build/lib -L/home/qwerty/ffmpeg_sources/fdk-aac/build/lib -L/home/qwerty/faac/output/lib -L/usr/local/lib/ -lrtmp -lpolarssl' --enable-version3 --enable-gpl --enable-nonfree --disable-doc --enable-yasm --enable-decoders --enable-encoders --enable-muxers --enable-demuxers --enable-parsers --enable-protocols --enable-filters --enable-avresample --enable-librtmp --enable-libfaac --enable-libfdk_aac --enable-libmp3lame --disable-indevs --enable-indev=lavfi --disable-outdevs --enable-hwaccels --enable-ffmpeg --disable-ffplay --disable-ffprobe --disable-ffserver --disable-network --enable-libx264 --enable-zlib --enable-muxer=md5 libavutil      54. 10.100 / 54. 10.100 libavcodec     56.  8.100 / 56.  8.100 libavformat    56.  9.100 / 56.  9.100 libavdevice    56.  1.100 / 56.  1.100 libavfilter     5.  1.106 /  5.  1.106 libavresample   2.  1.  0 /  2.  1.  0 libswscale      3.  1.101 /  3.  1.101 libswresample   1.  1.100 /  1.  1.100 libpostproc    53.  3.100 / 53.  3.100 Are the hoses in toilets in Asia something I should know about? I have noticed random bits of hose without proper fittings before I think for example in India and just assumed they are for use by the cleaners or for filling the water jug in .  But Now I'm travelling in Malaysia and Singapore and there are more western toilets than squat toilets in the places I've been yet proper hoses with proper fittings are very common in toilets:  (Hose next to a Western style toilet in my hostel in Chinatown, Kuala Lumpur.)  At one place in Singapore there were even signs on each cubicle door stating whether it contained a western or squat toilet, but also whether there was a hose! (I didn't take a photo of the sign, unfortunately)  This makes me think there is a use for the hose for clients, not just cleaners. But for what purpose? Should I know how to use it as a tourist? Please tell me it's not a kind of alternative to a bidet!  Possibly related is the fact that many toilet floors are awash with water. This can be a big problem if you're not wearing waterproof shoes or have to lower your trousers and keep them dry. Other than this toilets are pretty clean and I've seen both the hoses and the wetness in what I would regard as somewhat "fancy" places.