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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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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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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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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Confidence intervals and dividing by $n^{0.5}$

I am studying a-level and am confused when I divide the standard deviation by $n^{0.5}$ when doing confidence intervals. To put it another way when I don't divide by it? (where $n$ is the number of ...
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71 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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71 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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209 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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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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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 , ...
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28 views

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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58 views

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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39 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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41 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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18 views

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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287 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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210 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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16 views

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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63 views

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 ...
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603 views

Hypergeometric Distribution Probability (mean, variance, Std Deviation)

The distribution of the number of children per household for households receiving aid to dependent children (ADC) in a large eastern city is as follows: 5% of ADC households have one child, 35% of ADC ...
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229 views

How does standard deviation depend on data?

I've got a problem: I take a random variable, assign values to it and than I have to invent two different probability distribution functions with similar mean values (+-5%), but in the second function ...
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Calculate standard deviation from ratio of two variables

Ok here is my problem. For my research I am investigating if we can use twitter to create sports data. One part of the problem is for example this: We now for example that in the 6th minute of the ...
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117 views

Calculating minumum representative sample

Let's say I played 500 hands in poker and earned 345 units ( dollars not, important for calculation). So on long term I'm earning 345/500 = 0.69 * 100 = 69 every 100 hand session. But 500 hands is ...
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Getting the correct error for a mean calculation

A constant k needs to be calculated including its gaussian error. $k = f_{(u,t)}$ $k_i$ can be calculated with the values and errors of $u_i$ and $t_i$ and their respective errors. Main issue is ...
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Can't find Standard Deviation for Continuous Random Variable

Here is my homework problem. Again, sorry for the formatting: A continuous random variable X has a symmetric distribution with mean 18. A brilliant mathematician has estimated that the probability ...
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What are the bounds on Variance?

I have an image which can be considered as a 2D plane. Now, I have to check the variance of some points which are distributed over this 2D plane. TASK: I want to calculate the variance to predict if ...
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geometric standard deviation

The geometric mean is like the arithmetic mean on a log scale. with the arithmetic mean it is often useful to find the standard deviation. Can the same sort of thing be done to create a geometric ...
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28 views

Standard Deviation divided by Mean

I am comparing different lists of numbers to find the one which "varies least", in a common sense of meaning. Because the lists differ greatly in their mean value (some are around 0.3, others are ...
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Weighted Std Deviation of Securities

Corporate Finance problem - can't figure out if I'm right or not but here goes: Probability 15% 35% 20% 30% Security A 8% 5% -4% -6% I need to find mean and std deviation for security A. I got: ...
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Statistics: How to compute the probability density distribution of (µ1 / µ2) knowing only µ1, µ2, and standard deviations σ1 and σ2?

Given two means µ1 and µ2, and two respective standard deviations σ1 and σ2 (not variances or standard errors), how can I compute the probability density distribution of µ1/µ2? In my application, µ1 ...
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Function For Calculating Average Excluding Outliers

I'm looking for a function that will let me take an average and exclude outliers. Basically something where: 1, 2, 1, 2, 7 Would average out to 1.5. Would that be along the lines of standard ...
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What is the best distribution that describe the variances $\sigma^2(x)$?

I'm studying a numerical variances $\sigma^2(x)$. For each samples I have more than one hundred of variances. I'm looking for the distribution that can describe them. I think is not Gaussian, because ...
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Is Residual Standard Error the same as Residual Standard Deviation?

R's output gives you the Residual Standard Error but I am asked for the Residual Standard Deviation. Are those numbers the same? Also, how would you interpret the residual standard deviation? Thanks
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Probability and Standard Deviation Study Help

I am studying for a mid term that I have tomorrow with last years exam. I went through it and did as much as I could. These are the two questions I didn't get correct. The correct answers (given) are ...
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Math Expectations and Standard Deviations

Pizza Shop profits are $1, $3, and $2 for each sale of their small, medium and large pizzas, respectively. If these are the probability distributions Small Size: $1 - 0.40 Medium Size: $3 - 0.20 ...
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calculating a moving average rate for detecting an outbreak

I have a count for the number of occurences of a disease over a period of time. I want to set a threshold for detecting unusaul increase with a moving average. I am planning to use + 1,2,3 SD to set ...
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4 views

Error from bias and noise in a linear operator

There's a result $S$ that depends linearly on some forcing $F$: $S=\int dt' G(t-t')F(t')$ Let's say I need to predict $S$, but can't measure $F$ exactly. I have both bias and noise in my ...
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What is the probability of two things happening at the same time?

I am using the normal distribution for two events so there is a 34% chance of each event having one standard deviation above the mean. What is the probability of both events having one standard ...
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Biased estimator for the standard deviation

Question: If a distribution is equally likely to take the values 1 or 4, show that $s_{n-1} $ forms a biased estimator of sigma. I started this question by finding that: $E(X)$ = 2.5, $E(X^2)$ = ...
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Question composition rules in standard deviation

Standard deviation is defined as following: $f(x) = (\frac{1}{n} \sum_{i=1}^nx_i^2-(\frac{1}{n} \sum_{i=1}^nx_i)^2)^{1/2}$ Obviously, $(.)^{1/2}$ is not convex, so can I say $f(x)$ is not ...