What is Standard: Definition and 1000 Discussions

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter sigma σ, for the population standard deviation, or the Latin letter s, for the sample standard deviation.The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice, less robust than the average absolute deviation. A useful property of the standard deviation is that unlike the variance, it is expressed in the same unit as the data.
The standard deviation of a population or sample and the standard error of a statistic (e.g., of the sample mean) are quite different, but related. The sample mean's standard error is the standard deviation of the set of means that would be found by drawing an infinite number of repeated samples from the population and computing a mean for each sample. The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample size, and is estimated by using the sample standard deviation divided by the square root of the sample size. For example, a poll's standard error (what is reported as the margin of error of the poll), is the expected standard deviation of the estimated mean if the same poll were to be conducted multiple times. Thus, the standard error estimates the standard deviation of an estimate, which itself measures how much the estimate depends on the particular sample that was taken from the population.
In science, it is common to report both the standard deviation of the data (as a summary statistic) and the standard error of the estimate (as a measure of potential error in the findings). By convention, only effects more than two standard errors away from a null expectation are considered "statistically significant", a safeguard against spurious conclusion that are really due to random sampling error.
When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).

View More On Wikipedia.org
Recent contents Top users
  1. W

    B-L extension of the Standard Model

    i need what we mean by B-L extension of the Standard Model ?
  2. W

    The easiest way to standard model

    what is the the easiest way to learn standard model theory ?
  3. M

    Use standard identities to express

    Homework Statement Use standard identities to express sin(x+pi/3) in terms of sin x and cos x Homework Equations sin(a+b)=sinAcosB+sinBcosA The Attempt at a Solution sin(x)cos(pi/3)+sin(pi/3)cos(x) 0.5sinx + 0.8660cosx I'm just not sure if i need to simplify it even further...
  4. R

    Standard Matrix of Linear Transformation

    Homework Statement Let T: R3-->R3, defined by T(x)= a x x Give the standard matrix A of T, and explain why A is skew-symmetric. Homework Equations They define u x v as u x v=(det [u2 u3/ v2 v3], det [u3 u1 /v3 v1], det [u1 u2/ v1 v2]) For any vectors u,v,w in R3...
  5. M

    Sequences and convergence in the standard topology

    Hello all. I have to present a proof to our Intro to Topology class and I just wanted to make sure I did it right (before I look like a fool up there). Proposition Let c be in ℝ such that c≠0. Prove that if {an} converges to a in the standard topology, denoted by τs, then {can}...
  6. M

    What is the current status of particle physics beyond the standard model?

    In this forum, "Beyond the Standard Model", most of the discussion is about quantum gravity. But technically, even neutrino masses are "beyond the standard model". Some years ago, a paper was written, "The new minimal standard model", which self-consciously set out to describe a minimal new...
  7. K

    Redox Reactions and standard emf calculations

    What is the equation I should be using for the following question: At 298K a cell reaction has a standard emf of +0.17V. The equilibrium constant for the cell reaction is 5.5 X 10^5. What is the value of n for the cell reaction. Grateful for anyone's help!
  8. X

    Average of standard deviation makes sense?

    I've a set of tests, and for each test, they have different size. I'll show an example. Test1 size - Time(seconds) 100 - 10 100 - 23 100 - 17 200 - 37 200 - 42 200 - 47 300 - 53 300 - 53 300 - 53 For each test, I took the average. Average1 size - average 100 - 16...
  9. F

    Linear transformation with standard basis

    Homework Statement Let s be the linear transformation s: P2→ R^3 ( P2 is polynomial of degree 2 or less) a+bx→(a,b,a+b) find the matrix of s and the matrix of tos with respect to the standard basis for the domain P2 and the standard basis for the codomain R^3 The Attempt at a...
  10. A

    Determining Skew of Standard Deviations

    Determining Skew of a Data Set of Standard Deviations I currently have a formula to calculate the standard deviation of data using a sliding 20 period window which has allowed me to generate the histogram image seen below. My question is what calculations or formulas would I need to...
  11. A

    Compensating for outliers during Standard Deviation Calculation ?

    I am trying to calculate the standard deviation of a group of data based on a 20 period sliding window. I have run into a bit of a problem in knowing how to deal with gaps up or down in the readings and was wondering what the correct method for compensating for this was.Below is an example of...
  12. E

    Total standard deviation of a measured function.

    Hello folks, I've got a bit of a problem with estimating the overall error in measurement of a function which I have sampled at sixteen independent points and have calculated the associated error bar with each point. The problem is I'm not sure how to combine all the sixteen errors into a...
  13. B

    Which textbook for an introduction to the Standard Model?

    Hi. I am an undergraduate physics student and have just begun lectures on elementary particles and the Standard Model. At the moment I really know nothing about this branch of physics and am looking for recommendations on a textbook which introduces the subject well. Thanks
  14. K

    Understanding Brownian Motion: Statistics & Standard Deviation

    Can someone please explain how the standard deviation is relevant when we are talking Brownian motion? And why is statistics important when we want to understand the movement of a brownian particle?
  15. R

    Find 'k' (# of standard deviations from the mean)

    Homework Statement μ=10 σ^2=4 I seem to be getting the first two just time the same as i get every other problem, but I can't seem to get C)'s 'k'. typically i will take the absolute value of the portion that we are looking at, i.e. P(-10<X<10) would be |-10+10| = 20, divide that by two...
  16. B

    Standard conditions vs. Standard state

    What's the difference between standard conditions and standard state? I noticed in my thermodynamics chapter that in standard state, the reaction quotient is 1 because all activities are equal to 1 (if I remember correctly). Standard conditions is about standard temperature and pressure...
  17. T

    How Does Mixing Affect Entropy Calculations in Chemical Reactions?

    I know this is more of a chemistry question but it's come to this I'm afraid. When calculating entropy changes in chemical reactions sometimes we students of chemistry use standard molar entropies of the reactants and products. But this surely doesn't account for the mixing effect. e.g. N2 +...
  18. J

    Is the Standard Model a particle theory or a field theory?

    just looking at the standard model, which describes a host of fundamental particles and bosons, one could assume that the SM is a particle model. however, most of what i read appears to indicate that particles are merely "excitations" or manifestations of a field, and it has been stated on this...
  19. K

    Question about the standard model equation

    http://nuclear.ucdavis.edu/~tgutierr/files/sml2.pdf Where is the = sign in this equation? Does it have one?
  20. F

    What is symmetry breaking in the Standard Model?

    I'm trying to figure out where symmetry breaking occurs in Feynman diagrams. I'm just free wheeling here, correct me where needed. But as I understand it, when you have a Feynman diagram where there is an interaction of one particle which decays to others, the incoming particle may obey one...
  21. T

    How do we arrive at Q = -1 from T3 and Y?

    Im reading Peskin&Schroeder, chapter 20, the one that describes the Standard Model. I got the general idea, symmetry breakings and so on, but I am getting quite confused when starting to go to the first mathematical details. My doubts are when, in eq 20.69 defines Q=T3+Y and then forces that...
  22. D

    Standard normal limiting function chi squared

    Hi, I have a question If X1,X2,...,Xn are independent random variables having chi-square distribution witn v=1 and Yn=X1+X2+...+Xn, then the limiting distribution of (Yn/n) - 1 Z= --------------- as n->infinity is the standard normal distribution. sqrt(2/n) I know that Yn has...
  23. M

    Standard deviation and interquartile range

    Homework Statement There are 10 observations. (a) Suppose the IQR is 8. Is it possible that the standard deviation is 1? (b) Suppose the standard deviation is 8. Is it possible that the IQR is 1? Homework Equations IQR = R3 - R1 The Attempt at a Solution My argument is that (a)...
  24. J

    Linear Equations (General and Standard forms: From Wikipedia)

    Source: http://en.wikipedia.org/wiki/Linear_equation General form:- It says (under the title General Form) "If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis (where x is zero), is −C/B, and the slope of the line is −A/B."...
  25. C

    Why Do We Subtract 1 from n When Calculating Standard Deviation?

    ...I understand why it becomes more and more insignificant as the value of n increases, but what is the purpose of subtracting 1 from n in the sample population in the first place? Also, what is the purpose of squaring the result of x values minus the mean? I can do the problems. I'm just...
  26. S

    Question regarding certain standard integrals.

    Homework Statement OK, this is something that stumped me. Homework Equations \int_{}^{}{\frac{dZ}{ A^{2}-Z^{2}}} = - \int_{}^{}{\frac{dZ}{ Z^{2}-A^{2} }} Right? \int_{}^{}{\frac{dZ}{ A^{2}-Z^{2} }}=\; \frac{1}{2A}\ln \left\{ \frac{A+Z}{A-Z} \right\}+\mbox{C} \int_{}^{}{\frac{dZ}{...
  27. K

    Can the standard deviation calculation be generalized for other statistics?

    I've calculated the mean difference of my (normally distributed) data set. The mean difference is defined as: Now, I'm trying to calculate the "mean difference deviation" in order to generate a confidence interval for this quantity ( "95% of the differences in the set are greater than...
  28. B

    Calculating Volumes to Prepare Standard Solutions with KSCN

    Calculate the volume of each reagent required to prepare 25.0 mL of each standard solution at the specified KSCN concentration. Fill in the rest of the table (attached). My complete guess is that the solution II needs to be incremented by 2.5 ml each time.
  29. A

    Solving and presenting standard equations (software?)

    Hello General Engineering! I'm looking for a solution that will allow me to solve an equation (F=ma) by entering any two of the three variables, and then present that solution in a way that would be worth of reports/assignments. I'm currently requesting a trial of CSC Tedds, would love to...
  30. A

    Sample standard deviation proof

    Homework Statement Let x_{1},...,x_{n} be n observations. If y_{1},...,y_{n} is another set of observations s.t. y_{i}=ax_{i}+b , prove that s_{y}=|a|s_{x} . The Attempt at a Solution Attempt at a proof: Since \bar{y}=a\bar{x} +b then \bar{x}=(\bar{y}-b)/a and...
  31. P

    Calculating standard deviation from a confidence interval?

    Hello, I'm doing some nonlinear regression fitting, and I have a set of data with n data points and I am fitting the data to a model which contains 3 parameters. I can get a confidence interval from the program I'm using for each parameter, but how can I calculate the standard deviation for...
  32. T

    A little help understanding standard deviation & variance

    Hello all This is not homework, i work in engineering. I have some data in a table, there are 3 columns and 5 rows. The data relates to how high or low one rail is to the other. The data was collected across 3 days. At each 7m intervals the height of the right hand rail was...
  33. E

    Circuit schematics for standard parts

    Circuit schematics for "standard" parts Hi, I graduated from computer engineering, but I want to learn more about circuits. I did get the chance to play with Quartus 2 in some of my courses and I was wondering if there is a place where I can learn about the circuit schematics for the most...
  34. D

    Natural gas, Water, standard oil. say motor oil properties

    https://www.physicsforums.com/attachments/42263 https://www.physicsforums.com/attachments/42264 how we doing? i was just wondering does anyone have the properties of the following similar to the images attached.Natural gas, Water, standard oil. say motor oil properties.any oil properties...
  35. Y

    Editing PDF Files with 6.0 Standard Edition

    I want to get a program to edit pdf files. I notice there are still the old 6.0 standard edition available very cheap. Any short coming get that as I am too cheap to get the latest or even the 9 version. I am not trying to do video and all the fancy stuff, just want to create document with...
  36. B

    Standard Benchmark Problem for Computational Solution of Poisson Equation

    Hi, I am working on FEM methods as a part of my senior year project and I have written a poisson solver for the same purpose. The solver works pretty well on the simple problems that I have designed as of now and seems to give correct answer (i.e. the data matches the theoretical prediction) 1...
  37. C

    Can you make a solution under standard conditions?

    This is coming from junior-level physical chemistry. Lots of thermodynamic properties of reactions involving solutions are tabulated under standard conditions; I'm particularly thinking of standard half-cell voltages, but any property will do. How do you make, say, a sodium chloride...
  38. T

    Make Constructor for Standard Class

    How can I make a constructor for a standard class that accepts my class? For example, I have a class x and I want to make it possible to C++-style cast it to a string (ie "string(x)" rather than "(string)x"); how do I do that/what does the constructor function declaration look like?
  39. E

    Beyond the Standard Model (where *are* we going?)

    Alright, so I'm just getting through my first semester of QFT and while I'm not quite ready to step into anything really heavy, I'm close to the point where I can read introductory material on a technical level (like, I could probably start Zweibach's Strings for Undergrads). I've been reading...
  40. O

    What is the Standard for Valve Pressure Ratings?

    Hi, I have a question. Glove Valve PN16, JIS10k , ANSI 150#, AMSE, all they equal same, in withstand the steam pressure? I heard RN16 stand for 16bar pressure, but it's for steam too? I'm confuse.. million thanks if anyone would teach me please.
  41. X

    Standard Texts on EE Subfields.

    Anyone know standard texts for the following subfields that would be suitable at all for self-study? 1) Digital Signal Processing 2) Control Systems 3) Circuit Design 4) Communications (Digital & Analog, Wired & Wireless) 3) Probability & Statistics for EE. 5) Power Systems & Machines...
  42. T

    Standard Normal distribution probability

    Suppose X is the standard normal variable. is it possible to find P(X>x)? i.e does the function have a defined integral? How would you show that it is or is not defined? What information can we obtain about P(X>x).
  43. V

    Standard Harmonic Motion of a Plate

    A child with poor table manners is sliding his 240 dinner plate back and forth in SHM with an amplitude of 0.120 on a horizontal surface. At a point a distance 7.00×10−2 away from equilibrium, the speed of the plate is 0.370 . (a) What is the period (b)What is the displacement when the speed...
  44. M

    Question on mean and standard deviation.

    The length of time, t minutes, taken to do the crossword in a certain newspaper was observed on 12 occasions. The results are summarised below. Σ(t − 35) = −15 Σ(t − 35)^2 = 82.23 Calculate the mean and standard deviation of these times taken to do the crossword. My real problem is finding out...
  45. K

    Ki-Squared Goodness of Fit for Asymmetric Standard Deviations

    Hi To test the fitness of a certain model to some observational data I use ki_squared goodness of fit test. As you might know, this test is appropriate for normal distributions. In fact, one uses the standard formula: X^2 = Sum [(Oi - Ei)^2/SDi^2] Oi average of the ith bin Ei...
  46. P

    How Do Stoichiometric Coefficients Affect Gibbs Free Energy Calculations?

    Homework Statement For the reaction N2(g) + 3H2(g) <---> 2NH3(g) I am supposed to determine the equilibrium constant at 298K and 1 bar. We have been given a table that states that for NH3(g): \Delta_{r}G^{\Theta}= -16.45 kJ/mol I know that \Delta_{r}G^{\Theta}= \Sigma v...
  47. nomadreid

    How to get this integral into standard form

    If I have the definite integral of 1/sqrt(c2-dv2) (without a dv after it), with c a real positive constant larger than the upper limit of the integral, how can I get it into the usual form of an integral f(v) dv ?
  48. C

    What is the Significance of Standard Enthalpy of Reaction?

    http://en.wikipedia.org/wiki/Standard_enthalpy_of_reaction" of reactants (ΔHfO). My question is, why? And I also know that I can find http://en.wikipedia.org/wiki/Standard_enthalpy_of_reaction" (ΔHrO) by subtracting the bond energies of the reactants from the products. The result differs...
  49. C

    Stress energy tensor in extended standard model

    Maybe this is the wrong topic for this forum, but i am reading the following http://arxiv.org/abs/hep-ph/9703464 Which is on CPT violation and the standard model. I do not understand how they get to equation (9), when they write down the stress energy tensor as \Theta\mu\nu=1/2 i...
  50. W

    Stats 1 question: standard deviation

    I missed the lesson on this and i can't figure out how to do this question with the data given. Homework Statement A class of 20 students takes a test. The score, x , for each student was recorded by the teacher. The results of summarised by: ∑(x-10) = 208 and ∑(x-10)² = 2716 i) calculate...
Back
Top