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).
In the textbook Electrochemical Systems by Newman and Alyea, chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$ \mu_i = RTln(\lambda_i) \tag {1} $$
where ##\lambda_i## is the absolute...
I did some research online and found that "When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets." To explain this phenomenon, physicists invented the concept of spin. So far so good.
What I...
I started by expanding ##dx## and ##dt## using chain rule:
$$dt = \frac{dt}{dX}dX+\frac{dt}{dT}dT$$
$$dx = \frac{dx}{dX}dX+\frac{dx}{dT}dT$$
and then expressing ##ds^2## as such:
$$ds^2 =...
This is the question;
This is the solution as received;
I am not familiar with the approach used in the solution...my thinking was as follows
The frequencies are the same...the only thing changing are the discrete variables thus;
Let ##[x= 2,4,6]## and ##[y=7,13,19]## form a...
Assuming the Sun’s core has a mass of 0.35 Msolar_mass and taking values for other quantities from a internet background search or from the following figures
(i.e.: Radius "solar core" = 0.25 Rsolar_radius ):
------------------------------------------------------------------------...
Using this error propagation formula:
I expressed the standard deviation (s) and the partial derivatives of s w.r.t. each data point as:
This gives me an uncertainty of:
, where m is the mean. Does this seem reasonable for the uncertainty of the standard deviation? I also found the thread...
Is the Standard Model overfitted? I hear that the standard model is the most accurate model that we have so far showing accuracy of 13 digits or so. However I am wondering if this accuracy comes from adding so many constants until it fits.
First of all the standard model takes in 25 constants...
Hello everyone,
Our topology professor have introduced the standard topology of ##\mathbb{R}## as:
$$\tau=\left\{u\subset\mathbb{R}:\forall x\in u\exists\delta>0\ s.t.\ \left(x-\delta,x+\delta\right)\subset u\right\},$$
and the lower limit topology as...
Hi,
I’ve read military EMC standard (such as MIL 461) requires peak detection while consumer standard requiers average detection. Does it mean the peak detection is stricter than the average one?
First I'll give some context about how the book's written as many books are presenting it in different ways.
Reference: CRYPTOGRAPHY AND INFORMATION SECURITY, THIRD EDITION
By PACHGHARE, V. K.
Confusions:
1) Why is Expansion Permutation called so? The name sounds very contrary to what...
SR interpreted as having no absolute frame of reference and an absolute frame type version of SR, where the speed of light is isotropic only in one undetectable frame are considered equivalent, since they use the same math.
But here is a scenario in which I don't see how the physical predictions...
Hello, I noticed while trying to calculate the stardart gravity acceleration of the Earth that I never arrived at the defined value of 9.80665 m/s2 no matter that I calculate it with the equatorial radius, the polar radius, mean radius or the average of the equatorial and polar radius. With what...
I know there are some stationary 3d scanners like this, but they are really expensive.
When I saw, well an addition to handheld 3d scanner - a robotic hand, I came up with an Idea that same can be done with a simple camera, and photogrammetry. Found a nice article about photogrammetry on the...
If the standard model Lagrangian were generalized into what might be called "core capabilities" what would those capabilities be? For example, there are a lot of varying matrices involved in the standard model Lagrangian and we can generalize all of them as the "core capability" of matrix...
hi,
i have studied Standard Model for particle physics - at present it is described by three groups -
i have studied - these groups but could not establish what particular feature suggest of these group to be used to describe SM.
Thanks
Hello,
I watched MIT course on Nuclear physics (13. Practical Radiation Counting Experiments on ytb) and I do not understand why 2*sigma (standard deviation) = 0.05* countRate. As far as I know, integral of normal distribution from -2sigma to 2 sigma gives 95 % probability, but how can 2*sigma...
In Keisler Elementary Calculus page 39, example 4 it shows how to compute the standard parts of the following expression:
Example 4: If ##\epsilon## is infinitesimal but non zero, find the standard part of
##b=\frac {\epsilon} {5-\sqrt{25+ε}}##
Before calculating the standard parts the...
In a proof of a theorem or in mathematical writing generally, if there is a statement of a sub-theorem, does a proof always need to be given if 'obvious' or if obtained by inspection? Is there a way of saying "I got this by trying some numbers in a calculator and the pattern was clear"?
The...
Reference:
https://scitechdaily.com/breaking-cosmology-too-many-disk-galaxies-a-significant-discrepancy-between-prediction-and-reality/
The following are quotes from the reference.
1. The Standard Model of Cosmology describes how the universe came into being according to the view of most...
Is there a standard way to measure how far a system is displaced from equilibrium that can be applied to all physical systems? So, for example, a ball that is kicked, a spring that is stretched, a liquid that’s heated, and a charged battery are all systems that are displaced from equilibrium. I...
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.040403
In QM, I was taught that the imaginary unit ##i## in wave functions is merely a mathematical tool. It has no physical meaning. We can always take the real part of the complex wave functions. Therefore, there should be some...
Hi,
I obtain really high standard deviations in Excitation-Emission Spectra mainly for the phenolic compounds in olive oil (Em: 290-350nm).
Method:
I weigh 0.05g of olive oil and dilute it up to 25ml with cyclohexane to remain in the range of linearity for absorbance measurements to correct...
Find the textbook problem here;
Find the textbook solution here:
Now, to my question, did the textbook guys make an error on the value of ##σ?##, see my working;
Mean (##13## boys)=##\dfrac{153.4+(148.8×12)}{13}=149.15##
We know that,
##29.16##=##\dfrac{\sum x^2}{12}##-##(148.8)^2##
##\sum...
In English, does the equation
have any standard name besides (generalization of) the Euler-Lagrange Theorem? I have seen the designation "Euler-Poisson Equation" used by the Russian mathematician Lev Elsholtz way back in 1956 repeated in recent Russian webpages, but am not sure whether this...
Hi all - I wonder if you can help please.
Watching a video on youtube to help me understand about the mean, variance and standard deviation but last part of video left me confused.
The speaker said the following for the formula for standard deviation:
Consider if the variance is 200 for the...
My solution in shown on the attached files. The overall reaction between Mn02 is 0.81 Volts
The overall reaction which shows the reformation of the MnO2 catalyst is .27 Volts. The first reaction is more positive which shows that the MnO2 can work as a catalyst.
Hi! I'd like to ask you if my calculation of the amplitude on the mentioned process in the Standard Model is correct. The three diagrams contributing at lowest order should be
where in the middle one the two Higgs boson are NOT forming a quartic interaction vertex.
My attempt at calculating the...
b 90\% of the insects die after t hours.
(i) Represent this information on a standard normal curve diagram, indicating clearly the area representing 90\%
(ii) Find the value of \textbf{t}. $P(Z\le t) =0.9\quad Z = 1.282\quad t=57+(4.4(1.282))=62.64$ hours
\begin{tikzpicture}[scale=0.6]...
Determine the following standard normal (z) curve areas:
Determine the following standard normal (z) curve areas:
a. The area under the z curve to the left of $1.75$
from table $5\ \textit{$z^{*}$} =1.7 \textit{ col } .05 = .9599$
$\textit{ \textbf{$W\vert A$} input }...
Here is the report submitted
https://www.bbc.com/news/world-us-canada-57619755
"UFO report: US finds no explanation for sightings
The US government has said it has no explanation for dozens of unidentified flying objects seen by military pilots.
A Pentagon report released on Friday says of...
Chapter 1, Section 1.2
Write the standard form of the equation of the circle with the given characteristics.
72. Center: (−2, −6); Solution point: (1, −10)
Solution:
given: Center: (−2, −6); => h=-2, k=-6
=> then (x - (-2))^2 + (y - (-6))^2 = r^2
(x +2)^2 + (y +6)^2 = r^2...
I then use...
Chapter 1, Section 1.2
Write the standard form of the equation of the circle with the given characteristics.
74. Endpoints of a diameter: (11, −5), (3, 15)
I want to know if the following steps are correct for me to answer the above question.
Steps:
1. Find the distance between the points...
The mean of some data was 21.2°C, the standard deviation was 2, and the standard error was 0.8.
My textbook says that using one standard deviation, we would report the temperature of the substance as 21.2 ± 2°C, while using the standard error, the temperature would be reported as 21.2 ± 0.8°C...
A recurring topic in particle physics, is the possibility of a "desert" above the electroweak scale: no new physics (new particles, new forces) until the grand unification scale or the Planck scale. It's important to remember that the Higgs boson mass was correctly predicted three years in...
While I will not be showing the graph here, I am trying to dissect what the question even means.
While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any...
Hello!
I am taking a course on Electroweak & Strong Interactions (you could equally call it Standard Model I) and I find it absolutely fascinating! 😍
We studied how weak interactions violate parity, introduction to QCD, flavor physics (CKM matrix, CP violation, …) and neutrino physics...
Hello. Microphone is a simple device and its mechanism is also simple. The device converting sound waves into electrical energy is mic. But I am little curious about how microphone manufacturer company check their mics before selling? Means Can I test my mic at home using standard process? I...
In using scintillator or germanium energy sensors, certain radionuclides representing some definite line energies are used to calibrate the sensors. What technique or method is used to measure or determine the energies of these standards.
One of the distance measures in cosmology is angular diameter distance, that can be used to determine a distance to objects whose actual (spatial) size is known, i.e. standard rulers. Beside baryonic acoustic oscillations, do we know other objects (or maybe I should better say structures) that...
Hi,
Several times I encounter the argument that there is a "problem" with the masses in the Standard Model that we try to "understand". From the one side, you have people who ask why the neutrino masses are so small, and from the other side they ask why the top quark mass is so large. The...
Hi,
I'd like to integrate this function: $$ \int _0^ {\pi/2} 2 \sin(x) \cos(x) \sqrt {1+\sin^{2}(x) } dx $$.
I think I should introduce some substitution but I'm not sure. How should I proceed?
The mean is easy to calculate:
(x_m * 10 + y_m * 5) /15 = 5312
Which is correct.
But when you're suppose to calculate the variance it's impossible.
The values are squared so none of the equations will really help me..
I've slowly been writing a thread on octonions and particle physics, just to explain some facts in a self-contained way, with all the proofs. I don't know where this will lead. I'm certainly not presenting a theory of physics, much less advocating one. Mainly it's just fun.
Octonions and...
There has been a lot of talk about the value of beauty in theoretical physics. There seems to be a lot of little things that are beautiful because they make sense, according to what we already know, like the discovery of anti-particles, and recently the Higgs. The standard model was revealed...
Title says it all. Maybe it belongs more in Astrophysics but given the title...
"Beyond the Standard Model Explanations of GW190521"
- - - - https://arxiv.org/abs/2009.01213
If this is for real I'm surprised it's gotten so little attention..?
EDIT PS: (for my own convenience mostly) ...