Here is a question that combines uncertainties in measurements and significant figures.  Consider the following results to measure the value of g:  $$g={9.7,9.8,9.7,10.0,10.1,10.3}$$  Then to four decimal places $\bar{g} = 9.9333$, while the uncertainty of the mean is $$0.2422/\sqrt{6} = 0.0989$$  But clearly we would not quote these values as they stand.  So, what would be the statement of the mean value of g and its uncertainty to the correct number of significant figures? Would it be $\bar{g}=9.9 \pm 0.1$ or $\bar{g} =9.93 \pm 0.10$? The original measurements had two significant figures, but it would seem using the mean and its uncertainty would permit an additional significant figure. And what is the general rule for the significant figures for mean values and their uncertainties?
I have a number of measurements of the same quantity (in this case, the speed of sound in a material). Each of these measurements has their own uncertainty.  $$ v_{1} \pm \Delta v_{1} $$ $$ v_{2} \pm \Delta v_{2} $$ $$ v_{3} \pm \Delta v_{3} $$ $$ \vdots $$ $$ v_{N} \pm \Delta v_{N} $$  Since they're measurements of the same quantity, all the values of $v$ are roughly equal. I can, of course, calculate the mean:  $$ v = \frac{\sum_{i=1}^N v_{i}}{N}$$  What would the uncertainty in $v$ be? In the limit that all the $\Delta v_i$ are small, then $\Delta v$ should be the standard deviation of the $v_i$. If the $\Delta v_i$ are large, then $\Delta v$ should be something like $\sqrt{\frac{\sum_i \Delta v_i^2}{N}}$, right?  So what is the formula for combining these uncertainties? I don't think it's the one given in  (though I may be wrong) because it doesn't look like it behaves like I'd expect in the above limits (specifically, if the $\Delta v_i$ are zero then that formula gives $\Delta v = 0$, not the standard deviation of the $v_i$).
pyvenv vs venv vs python-virtualenv vs virtualenv and python 3 malikarumi@Tetouan2:~$ pip install virtualenv     Collecting virtualenv     Downloading virtualenv-12.0.7-py2.py3-none-any.whl (1.8MB)     100% |################################| 1.8MB 330kB/s   malikarumi@Tetouan2:~$ pip freeze     (a lot of stuff, but not virtualenv)  malikarumi@Tetouan2:~$ virtualenv testvenv1     The program 'virtualenv' is currently not installed. You can install it by typing:     sudo apt-get install python-virtualenv   What is going on here? is python-virtualenv == pyvenv? Isn't that still broken? Does original virtualenv still work with python? if venv (too many name variations!!!) is part of the standard library, , why am I being told to install it?  And when I did try to install it, I got:  malikarumi@Tetouan2:~$ sudo apt-get install python-virtualenv     Reading package lists... Done     Building dependency tree            Reading state information... Done     The following extra packages will be installed:     python-colorama python-distlib python-html5lib python-pip python-setuptools   At which point I aborted, because installing python3-pip just before that had given me   Setting up python3-setuptools (3.3-1ubuntu1) ... Setting up python3-pip (1.5.4-1) ...   And I wasn't sure if the extra packages would overwrite them or go onto python 2.7.  I read that python 3 is supposed to be the default going forward. Since both 2.7 and 3.4 are there, and have separate commands, how do I not only make sure Python 3 is my default, but that anything I install goes there and is used by it instead of 2.7?   BTW, I tried sudo apt-get python3-virtualenv and got: E: Unable to locate package python3-virtualenv Why is "bicycle" pronounced differently from other obviously related words? Simple image editor? I want to encrypt a USB stick, and be able to decrypt it on Windows as well as Ubuntu. How do I do this &amp; what programs do I need to use? Benevolent aliens who (initially) refuse to show themselves This is a sci-fi book where aliens arrive on Earth and push Earth towards world peace, but refuse to reveal themselves physically. When the aliens finally do show themselves, we find that they       look like .   I recall that the aliens seemed benevolent, but that humanity did not like the direction they were being told to go. I cannot remember the ending or if the aliens turned out to be truly benevolent. How do I set the default program? How do I set the default program that I use?  I have tried to open System Info → Default Program → change my program, but it won't work,  Any idea? Or should I use Terminal?   I want to replace the default movie player with VLC media player, because the current movie player is useless to me. Can I deploy Juju on Eucalyptus? Please let me know if I can deploy juju on Eucalyptus, if yes please provide me the configuration details which i need to edit on environments.yaml file. i want to add watermark on some videos but problem is because image in some videos its too small and in some videos its too big, (i think it depends on input link resulution)   so all my videos have output '640:360' so how can i make watermark image to be same in all videos not on some videos smaller in some bigger   ffmpeg -i "link" -i "/var/www/logo/logo1.png" -filter_complex 'overlay=10:10' -vcodec h264 -crf 25 -preset superfast -maxrate 600k -bufsize 600k -aspect '640:360' -s '640:360' .... Working in Cycles.  Say I have a "disco ball" with a glossy shader. I'm pointing a spot light to it, and I'm trying to have the reflections of that light illuminate the diffuse material on the walls with the patterns from the ball.    I get this:    but I'd like to get something like:    For the illustration I placed a point light inside the ball an removed faces. But what I'd like to do is move the light around the ball so that the light reflected from it changes like it would do in real life.   Is that possible at this point?  EDIT:  Just for the record here's the image rendered in LuxRender (yet another program to learn...) Mouse Pointer Locator Due to a stroke, I have had some vision impairment in that I sometimes have a hard time locating my mouse pointer on the screen.  I have tried making the mouse pointer larger which helps but is still not the solution.  I am new to the Mac world and would appreciate your help.  In Windows, there is an option where pressing the CTRL key will help to identify the mouse pointer using a temporary display of several radiating concentric circles around the mouse pointer.  Is there something like this on OS X? How can I create that glitter tears effect and the sparkles? Sending email with PHP from an SMTP server How to implement Bitcount using only Bitwise operators? Got this as homework and I don't know how to tackle this. Help please!  Prove that the isometries of $\mathbb{S}^{n} \subset \mathbb{R}^{n+1}$, with the induced metric, are restrictions to $\mathbb{S}^{n}$ of the linear orthogonal transformations. How does extra damage work for critical hits? I'm a bit confused on how extra damage works for critical hits. Let's take the following example: A thief with sneak attack rolls a crit. I'm under the impression he rolls double his normal attack damage dice AND double his Sneak Attack damage dice. Is this accurate? Another example, I finished DM-ing my first campaign recently. The Giant Spider enemy monster has an melee attack that causes a constitution saving throw. If the player fails, the enemy rolls an additional 2D8 of damage. In this situation, if there was a critical hit, and the player failed their saving throw, would I also roll double dice on the additional damage? Or is that considered a separate attack? Checking if Ubuntu package contains desired update I want my Qt application to be able to save simple vector graphics to clipboard in a compatible way. On windows I want to be able to paste the graphics into Microsoft Word or Powerpoint. On Linux I want to be compatible with the Open Office.   Which format would you recommend? Can Qt generate EMF in an easy way? Is SVG an option?  Update:  My current plan is to add a piece of native win32 code to render the graphics to emf on windows. This code will not be available on linux. I have a sample composed by 2500 count data values. I've plotted in R the corresponding histogram and ecdf. I've run the One-Sample Kolmogorov-Smirnov test to check if the distribution is either exponential or poisson, but I got negative results.  Is it possible that the One-Sample Kolmogorov-Smirnov test, it's not the correct test to work with this count data.  What is the best way to identify a distribution for this kind of data? How to approach the modeling of duct work, piping, wiring? How to prove the continuity of the metric function?