I'm trying to find out how accurate percentile is. I have used scipy.stats to calculate the rank of percentile. However, it doesn't match the one I have coded.  I have a few questions. Say 25th percentile. Does it mean, equal or below 25th percentile or below 25th percentile? Now please have a look at the code and I will try to explain why I am confused.  import numpy as np from scipy import stats  def percentile_score(arr, n):     o = 0     for a in arr:         if a &lt;= n:             o += 1     return np.round(o / len(arr) * 100, 2)  def percentile_test(min_val, max_val, total, seed=0):     if seed &gt; 0:         np.random.seed(1)     r = np.random.randint(min_val, max_val+1, total)     p1 = percentile_score(r, 1) # calculate percentage of &lt;= 1     p2 = percentile_score(r, 2) # calculate percentage of &lt;= 2     p3 = percentile_score(r, max_val) # calculate percentage of &lt;= max     print("Min / Max                    : {} / {}".format(np.min(r), np.max(r)))     print("#1 count vs percentile       : {}% vs {}%".format(p1, stats.percentileofscore(r, 1)))     print("#2 count vs percentile       : {}% vs {}%".format(p2, stats.percentileofscore(r, 2)))     print("Number #50 probability (&lt;=)  : {}% vs {}".format(p3, stats.percentileofscore(r, 50)))  percentile_test(1, 50, 1500, seed=1)   OUTPUT  Min / Max                    : 1 / 50 #1 count vs percentile       : 2.13% vs 1.1% #2 count vs percentile       : 3.8% vs 3.0% Number #50 probability (&lt;=)  : 100.0% vs 99.26666666666667   If percentile necessarily means &lt;=, then #50 must be 100% if it means &lt;, in this case #1 must be 0  Also the calculations I have found don't match with the expected value. What am I  missing here?
Given the following data:  972, 975, 985, 993, 993, 995, 998, 1001, 1004, 1007, 1008, 1009, 1011, 1015, 1016, 1020, 1022, 1032  I calculate the lower quartile as follows:  Number of values: 18, Number of 'gaps': 17.  Lower quartile is at 17/4 + 1 = 5.25th value. 5.25th value is 993 + (995 - 993) x 0.25 = 993.5  Upper quartile is at 3 x 17/4 + 1 = 13.75th value. 13.75th value is 1011 + (1015 - 1011) x 0.75 = 1014  Both the Excel QUARTILE function and the R quantile function agree with me. However the book I am using (Understanding Statistics by Graham Upton and Ian Cook) give different answers (993 and 1015 respectively). I'm confused. Which is correct?
I've often come across posts on forums or other websites where you see people joking in such a manner about running/logging in as root as if it's something awful and everyone ought to know about it. However, there isn't much that a search reveals on the matter.   It may be widely known to Linux experts, but I really don't know why. I remember always running as root when I first tried Linux years ago (Redhat and Mandrake) and don't remember running into any problems because of that.   There are actually some distros that have a bright red background with alert signs all over it as wallpaper for the root user (SuSe?). I still use the "Administrator" account for regular use on my Windows installation and haven't ever run into any problems there either. I have been stuck in a problem, that has thrown my brain out of the coding. This problem is at very high priority and I need the solution as early as possible. Problem is as :  There are exactly N advertising boards on the highway. Now a company want to advertise on some of these advertising boards(each advertising board costs some money) .  Company strategy is that, they want at least 'K' advertisement should be there among M consecutive advertising boards. But at the same time Company want to pay minimum for its advertisement .  Now, what is the total number of ways, different ways Company can advertise meeting its minimum cost strategy.  As for Example: N= 3, M = 2, K=1 ==> there is only one way for minimum cost, ie. 0C0 , where '0' denotes No company advertisement, and 'C' denotes company advertisement board.  Similarly, for N =4, M =2, K =1 ==> there is 3 possible ways, ie. C0C0, 0C0C, 0CC0.  Hope to get a reply from someone soon. Thanks. Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$ if $x,y,z$ are positive real numbers,Prove:$$3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$$ Additional info:$\sum_{cyc}$ denotes sums over cyclic permutations of the symbols $x,y,z$. I'm looking for solutions and hint that using Cauchy-Schwarz and AM-GM because I have background in them.  Things I have done: Writing Left hand side in expanded form:$$LHS=3(\sum_{cyc}x^3y^3+\sum_{cyc}xy^4z+3x^2y^2z^2)$$ Right now I don't have good idea were to start(Is expanding and looking for AM-GM is good?).So any hint is appreciated. Source : This inequality can be found as Problem 42, page 13, in the book &quot;Old and New inequalities&quot; by Titu Andreescu, where it is attributed to Manlio Marangelli. I'm talking about the movie  Spoilers ahead.  Walter (Daniel Radcliffe) gave the task or blackmailed the Four Horsemen to steal a chip from a lab which can access any digital device. So they did steal the chip. And when they rescue Dylan Rhodes (Mark Ruffalo) from drowning in the water, Jack Wilder said that the chip is fake.     Jack: Wait something is not right.      Atlas: What's wrong?      Jack: It's fake.   Then they assumed that Walter did not know that the chip is fake. So they came with a plan to bluff. They pretended that they had the real chip. After they got caught by Walter, they gave the fake chip to Walter. Walter checked the chip and declared it as real. The Four Horsemen were surprised.     Walter: I'm sorry to interrupt. But I have to say congratulations and   thank you. It's real.      Lula: What? It's real!!!!!      Atlas: What? Is it real?      Jake: What is he talking about?   What happened? I didn't get it. What did I miss? Was the chip real? Was Walter pretending it to be real? If so, then why? If not, who switched the real chip with the fake one? Who had the real chip before? How to install packages in ubuntu without internet connection? Dealing with rust on a steel frame If light is an electric and (magnetic field), how can it be absorbed? I was wondering how light or any electromagnetic radiation can be "absorbed" if it consists of electric and magnetic fields. For example if there is a charge at point A, and the  light reaches point A, it will cause that charge to move depending on the value of the electric field. However, why wouldn't this electric field continue on and influence others particles everywhere else? For example, if you have a static charge creating an electric field, then if you put a charge at point A it will feel its effects and then if you bring a charge at another location B it will also feel its effects, namely it will not have been absorbed. Please shed some light on this. Thanks  edit: Does this mean the electron that absorbs this light moves in such a way that it creates an electric field of its own canceling the initial one? Or am I way off? Database Design Best Practices undelete big files - mission impossible? I've accidentaly deleted outlook.pst (6.7GB) file, while there was only 400MB free space left on primary NTFS partition (winxp).  I've tried several recovery tools to get this file back. "Ontrack Easy Recovery Pro" found 0 pst files (complete scan mode), while "Recover My Files" in sector scan mode found 5 pst's, but 4 of them of sizes from 3 to 28 KB, while the 5th one - 1Gb.  I've managed to succesfuly recover 1Gb pst file, which was 1 year old copy (the one used after the latest windows reinstall).  Now, I'm frustrated and confused   Why 1 year old file was succesfuly recovered if there were only 400MB left on primary partition? Where's 6.7GB file gone? I did some reading (), and it seems that there's almost no probability to retrieve the file I'm looking for, but wait - none of recovery tools i've used found zero-sized pst file, moreover - if due to fragmentation a file might be corrupted - we could use scanpst.exe to fix some errors and survive with 10 or 100 emails missing - whatever. Could you please recommend some more sophisticated recovery tools for this particular task?   Appretiate your help - thanks in advance Can you give us some way to access pending Reviews for a post from the post itself?  I think this would also help improve the accuracy and quality of reviews done, as users that come across the post naturally are more likely to be better qualified to evaluate the post, and are already taking the time to understand the post's content anyways.  In most cases, these users will be able to provide better reviews than those who are  [often quickly] going through the Review Queues.  In addition, I think it would help get more reviews done, as someone viewing a post through normal site usage would be more likely to take an interest in helping maintain that post. I know I definitely would be more active with this instead of having to go through the massive Review Queue. The task of helping fix one question that I am currently reading is far more do-able than cleaning up a large queue of questions that is largely full of content I don't care about.  I'm thinking of something like a reviews(1) link that is accessible from the post itself that appears based on your rep, or perhaps even on your rep within the post's tags. Manually disable a module Suppose I have a node in the shape of a circle. How can I make its border thicker?   \node[circle, draw=blue!80, inner sep=0pt, minimum size=12pt] (1) at (0,0) {1}; I have observed that in gedit if I edit a file, another file is created in the same directory (the one with the same filename and a tilde '~' suffix). The extra file remains even if I close gedit.  I understand the need for a temp file (eg. in case of a crash), but vim for example deletes the extra file it creates, when I close it.  Is there a way to do the same with gedit? Some configuration perhaps? Why are we using the squared residuals instead of the absolute residuals in OLS estimation?  My idea was that we use the square of the error values, so that residuals below the fitted line (which are then negative), would still have to be able to be added up to the positive errors. Otherwise, we could have an error of 0 simply because a huge positive error could cancel with a huge negative error.  So why do we square it, instead of just taking the absolute value? Is that because of the extra penalty for higher errors (instead of 2 being 2 times the error of 1, it is 4 times the error of 1 when we square it). I came across this example when trying to mount a usb device inside a openvz container and I have never seen the construct in the second line before. Can you explain what it signifies?  #!/bin/bash . /etc/vz/vz.conf Input file in chapter title I cannot figure out how to import a file in a chapter title:  \chapter{\input{"Introduction.txt"}} \chapter{\texorpdfstring{\input{"Introduction.txt"}}{Introduction}}   Both of these fail with      Use of \@chapter doesn't match its definition.   Any help will be greatly appreciated. How to read command line arguments of another process in C#? How can I obtain the command line arguments of another process?   Using static functions of the System.Diagnostics.Process class I can obtain a list of running processes, e.g. by name:  Process[] processList = Process.GetProcessesByName(processName);   However, there is no way to access the command line used to start this process. How would one do that? Is it possible to make my laptop's screen act as a second monitor for my desktop computer? From what I know, it is unknown whether $x_n=x_{n-1}^2 + 1$ has a closed form. Is there a recurrence relation which is known to have no closed form with a proof of inexistence?  Assuming a closed form is a non recursive description using the elementary operations of addition multiplication and power, or, assuming any other good definition of "closed form".  Edit  There are similar questions out there, but the answers are a little bit going around the question.   So is there one with proof or is it unknown? And if it depends on the definition of a closed form, then what are the (or some) options? How strong can a closed form definition be to still have a recursive relation that can be proved to not being able to have its form?  Update  Because it is a big question, and I don't want to open a new small one, I think a good representative small question about this subject is:  Is there a recurrence relation with a domain of the natural numbers, described by elementary functions, which has no closed form defined as:  A closed form of a recurrence relation with a domain of natural numbers is a function $f$ that can be described as a composition of a constant number of elementary functions without reccursion. i.e, $f(n) = f_1(f_2( \dots (f_k(n))) \dots) $ where $f_i$ is elementary for all $1 \leq i \leq k$   I think this definition is the most intuitive and basic.  For example, the relation $x_n = x_{n-1}+1$ has a closed form in this sense: $$f(n) = f_1(f_2(f_3(f_4(n))))$$  Where $f_1$ is division, $f_2(n)=(n,2)$, $f_3$ is multiplication and $f_4(n) = (n,n+1)$   Is there a recurrence relation which has no closed form in this sense? I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject.