In Probability and Statistics, the standard deviation of a statistical population or data set is a measure of how much variation or dispersion exists from its average value. It is defined as the square root of the variance.

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Relationship between exterior power of representation and variance?

I was reading the question: Symmetric and exterior power of representation regarding how to determine the character of an exterior power of a representation from the original representation. One of ...
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Removing slope from running times

First of all, & looking at the suggested question list, I hesitate at asking this basic question: Here goes. I'm trying to assess my fitness, and I need a bit of mathematical help. I do a little ...
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Relation between standard deviation and mean in random processes

In a Poisson distribution the square of the standard deviation $\sigma$ is equal to mean $\mu$ ($\sigma^2=\mu$) and in a binomial distribution $\sigma ^2=\mu\,(1-p)$ (with $p$ the probability of ...
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Understanding the Normal Distribution?

If a sample is normal with observations independent and identically distributed: $\mu|\sigma^2 \propto N(\beta \,,\,\sigma^2/\, n_0)$ How can I show that $\mu\,|\,x_1,x_2,....x_n\,,\,\sigma^2 \sim ...
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Definition of Standard Deviation

We note that given a probability distribution function $P$ over a space $U$ the expected value of a function of the elements in U: $$ E(f(x)) = \int_{U} f(x)P(x) $$ We thus consider the mean as the ...
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Standard Deviation of 2D vector data

Given a sample set of wind data (speed and direction parallel to the earth), I would like to identify the consistency of wind samples. Standard deviation comes to mind, but I don't know if it is ...
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183 views

Bayesian Shrinkage Factor

Vasicek(1973), referenced in this paper(See bottom of page 16) explains a method of shrinking individual betas $\beta^{TS}$ toward a cross-sectional mean $\beta^{XS}$ as follows: for each time $t$, ...
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93 views

Model selection: geometric mean of the standard deviation.

I have two models that represent a physical process. To determine which model is the best, I make some experiments and compare measured data with data predicted by each of the models. The model with ...
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76 views

Have averages, need variance

I have a large spreadsheet, generated by a colleague, that contains the results of $E$ experiments. For each experiment, he calculated the average of $M$ measurements. I need the calculate the ...
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274 views

rate of convergence of mean ,variance & skewness estimators

We are asked a question which of mean,variance or skewness converges faster. At first I thought it was straight forward answer: mean->variance->skewness. But I am not sure anymore because I read ...
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516 views

How can I compare two averages of imperfect measurements, with their std. deviations?

I have a process by which I measure the times it take to do something, (run some code), and this time varies, a lot. I'm trying to optimize this code, making small changes that sometimes have small ...
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Help with problem: Estimated Standard Deviation of Regression Equation (Simple Linear)

This is a practice problem. I've solved part (a). I have provided verified answers (from the published key) to all parts (a), (b) and & (c). I need help solving (b) and (c). Consider a simple ...
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Caclulate Standard Error when subtracting two effects

I am working on this issue that compares two regions with the McCrary Test (Regression Discontinuity Design). It basically measures how the density of a variable of interest develops accross a pre set ...
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Combining standard deviations - given mean, sample size, and SD of two sets?

I have two groups A and B. I know A and B's sample sizes, mean performances on a test (not their individual scores however), and the standard deviations of A and B. I know how to combine them to find ...
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37 views

Relevancy of standard deviation

I'm a maths student but I'm a bit of a retard when it comes to probability. I have this very basic question in mind : Why is standard deviation defined as the square root of the variance, when surely ...
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34 views

Calculating a three sigma limit on data

So I have a list of data points each with their own error (eg. 3 +/- 0.2 units) and I want to determine which of the data points are within 3 sigma. To do this do I just calculate the standard ...
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25 views

Variance of exponential moving average

I'm not quite sure what the form for the rolling recursive variance should look like. I have that the recursive average is $m_t = \alpha x_t +(1-a)m_{t-1}$. Then would the rolling recursive variance ...
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35 views

deriving mean-variance form

I have a function $$W(x_1,x_2,...,x_n)=A\sum_{i=1}^{n}x_i^2+\sum_{i\ne j}^{n}x_ix_j,$$ where $A \in[0,1)$. And in a paper I am reading, $W$ can be written in the "mean-variance" form:$$n(n+A-1)[\mu^2(...
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Chebyshev Inequality, possible range of 90th percentile of a 100-vector with rms(x)=1

My lecture notes states the Chebyshev inequality as follows: If k is the number of entries of x that satisfy $|x_i − avg(x)| \ge a$, then $k/n \le {(std(x)/a)}^2$. x is a 100-vector with rms(x)...
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Standard error of the estimate

Question: In order to estimate the total weight of rice of 100 bags, a sample of 25 bags was weighted, giving the average weight of 50 kg. If the population standard deviation is 1.5 kg, estimate the ...
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182 views

Am I on the right track with this question on standard deviation?

The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean? ...
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78 views

What is the difference between root mean square, and standard deviation?

I am currently working through the Feynman Lectures, chapter 6: Probability. I have reached his problem of the "random walk". After deriving this and getting some root mean square, wouldn't this ...
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I need help with this Standard Uniform random variable problem

Click here for problem image I need help on how to do b,c and d. Can I please have an idea of how to start it because i have no idea how to do this.
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Does the standard deviation of a normal distribution change when looking at a shorter period?

Say we are given a normal distribution with mean $\mu$ and standard deviation $\sigma$, where $\mu$ is the expectation in time period $T$. Now, say you need to use the distribution over a shorter ...
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Distribution of ratio of 2 points drawn from normal distribution?

Let's say we have a known normal distribution $N(\mu,\sigma^2)$. I now draw 2 points $p1$ and $p2$ randomly from this Gaussian distribution for every observation, and repeat this process large number ...
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How to find the +/- error of a radial average?

I have a set of directions in degrees in which I want to find the average and the distribution error. At the end of the day, I want to say something like: "Given these 100 directions, the average is ...
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How to compare standard deviations of different sample sizes

I am interested in estimating the value of an unknown, random variable, X. X changes over time. So, X = X(t) = Xt At specific time intervals, I estimate the value of Xt using 7 different methods. Some ...
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33 views

Statistics,standard deviation,spread,gemoetric meaning

What are the geometrical interpretations/meanings of these statistical quantities: mean, standard deviation and spread?
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54 views

Portfolio sd, covariance over different time periods

So we are trying to forecasted portfolio return and deviation of a historic set of investments, we have different lengths of data for different investments. My boss calculated the covariance using the ...
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21 views

Finding the Correct Sample Size N to calculate the $SEM$ in a Relative A/B Test with $X \sim B(p_1,n_1)$ and $Y \sim B(p_2,n_2)$

I asked a similar question on Cross Validated but since I'm more interested on the theory behind choosing the right $N$, I decided to also post it here. For the test, I randomly assign users to two ...
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195 views

A Gaussian Divided by a Gaussian Equal to A Gaussian Divided by a Constant

I have a neural-network model in which each neuron is associated with an angle $\theta$. Firing rate as a function of $\theta$ is either a Gaussian or a constant. The claim has been made using this ...
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18 views

Lower std.deviation of a distribution?

How would one lower the std.dev => $\sigma$ for an arbitrary distribution? The reason why I ask, is because I have a distribution which tend to get far above my threshold value, and i am running out ...
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Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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Combining standard deviations

We have two groups measuring the same resistors, the nominal value is unknown. Group 1 is slower and because of that they did not calcute the s1 empirical standard deviation. Group 1: N1=500 , R1=...
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Standard deviation of the mean through bootstrap resampling of dependent samples

I'm trying to do a Monte Carlo approximation of an integral where the samples are not independent (how much so can be tuned by a parameter giving how often I sample). Therefore the regular expression ...
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Mean for seat allocation

There are a set of kids (let's say 30) asked to sit in a row of seats, leaving at least one empty seat between them until all seats are filled. At the end, how do I calculate mean of the fraction of ...
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122 views

Problem understanding Standard Deviation calculation

For a given dataset wm_t, the example for calculating standard deviation of the "gain" column is represented as: ...
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908 views

Standard Error of Sample Variance

I have a time-series of values $X_1, X_2, \ldots, X_t$, for which I compute sample variance: $$\hat{\sigma}^2 = \operatorname{var}(X_1, \ldots, X_t)$$ (unabiased estimator using $\frac{1}{t-1})$. ...
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statistically analyse pass rate of test in different locations

I'm looking to analyse some data and as it's been a long time since my statistics days I'd like to know which area of statistics my problem lies. Lets say I have a number of different driving ...
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Welford's algorithm for standard deviation: combine multiple sets of results

Suppose I use Welford's algorithm to compute the standard deviation of multiple sets of values. I only store all the n, mean and M2 results that the algorithm calculates, thus I have these three ...
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How to 'adjust' a series mean to match another series mean

I have 2 data series that I would like to compare. Perhaps it's best to show a graphic of the series as they are now ... and what I would like to do ... Basicaly, I would like to visually ...
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Uncertainty of measurement with goniometer

I got a goniometer with scale -90 to 90 degree. I use only 0 to 90 degree. One section of the scale has 1 degree. I read a value of $62^\circ$. What is the uncertainty of this measurement? I thougt ...
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Finding groups with minimum mean deviation

Is there any algorithm that groups consecutive elements in an array that gives the minimum mean deviation. For example we are given an array a=[1,2,3,4,8,2,3,5] There can be many "consecutive" ...
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Population confidence interval from sample SD and sample mean?

A sample has: $$\text{a sample size } n = 70,$$ $$\text{sample standard deviation } s = 184.43,$$ $$\text{and a sample mean } \bar{x} = 564.15.$$ Compute a 95% confidence interval for the population ...
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495 views

Monte Carlo standard deviation of the mean estimate too small.

I'm doing a Monte Carlo calculation and use the standard deviation of the mean $\sigma_M$ as the error. To get an estimate of this from the regular standard deviation I use $$\sigma_M=\dfrac\sigma {\...
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391 views

Is it possible to convert calculate the percentile and t-scores from mean and standard deviation?

I need to produce a table that will allow you to look up various types of scores for a test using the number of correct answers like this: ...
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Any way to simplify this expression?

So I have a vector of asset allocation weights given by $x \in R^4$ and a covariance matrix of the asset returns $\Sigma \in R^{4,4}$. I know by the spectral theorem, $\Sigma = V DV^{-1}$ and the ...
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standard deviation of a rate of phone calls

I am trying to implement some real time monitoring. I have a real time data feed from which I can calculate the number of phone calls received in the last hour (now-60 minutes). I want to alert when ...
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Why is my sample standard deviation not an unbiased estimator?

I was goofing around with a spreadsheet and decided to show empirically that the sample standard deviation is an unbiased estimator of the true population standard deviation. Link to Excel File I ...
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Probability for Rolling 10 tethedrons 100 times

I am pretty confused about how to form the probability distribution function of the following question: Suppose you have a tetrahedron with numbers 1,2,3,4 on respective faces. If you roll 10 such ...