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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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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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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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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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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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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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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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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problem on standard error in sample data

From a population of 20,000 observations, a sample of 500 observations is selected. how to Calculate the standard error of sample mean if the population standard deviation equals 20.
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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 ...
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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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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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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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Collection of values: Root mean-square?

I am currently developing a music recommander system using the Million Song Dataset. This dataset contains 1mio songs and around 50 attributes related to them (how hot it is, the tempo, the key, the ...
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Prove the expression for standard deviation

Problem Let $x$ be a variable assuming the values $i=1,2,\ldots,k$ with frequencies $f_i$ and let $F'_i$ be the corresponding cumulative frequencies of the greater-than type, while $F''_i$ are ...
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How to interpret Standard Residual Deviation?

have fitted regression lines for 200 data sets where each data set contains 40 data points.As a result of that now I have 200 Standard Residual Deviation values and need to interpret that results. How ...
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Mean of standard deviation and confidence intervals

I have 1000 values from which I calculate the mean A and the standard deviation std A and the 95% confidence interval. I have another 1000 values from which I calculate the mean B and the standard ...
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How to check null hypothesis in Minitab without specific data?

I have been given a question that specifies a sample size of 50, sample mean of 3.05, standard deviation of .34, and desired mean of 3.2. The question asks whether or not the average mean is ...
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Is there a rule for choosing mean or median for missing data?

I have a dataset with missing data foor different features. I wanted to fill this empty cells with mean or median of present data of these features, but what should I chose? Median seems to be better ...
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What is the probability that in a random sample of 25 students from this group will be between 73 and 75?

The mean height of a group of 500 non-smoking college students is 74 inches and the standard deviation is 5 inches. What is the probability that in a random sample of 25 students from this group, the ...
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Shrinkage of variance

I have a sample of N variables, and a sample period of length T. At each time $t$, I have the following information: For each variable i, I have an estimate of variance $\widehat{\sigma^2_{i,t}}$. ...
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Proof for Bessel's correction

I have a question regarding a proof for Bessel's correction As a background fact, we use the identity $E[x^2]=\mu^2+\sigma^2$ which follows from the definition of the standard deviation and ...
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Application of Statistics in Sports Pool Selection

I am looking for the best mathematical approach for my hockey pool selection based on statistics from the previous season. We are 8 participants. Each participant must select: 9 Forwards 4 ...
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How do I set a problem like this up in my calculator?

"It is known that Lemmings (a small rodent like creature) have a mean body weight of 63.5 grams with a standard deviation of 12.2 grams. If the weights are distributed normally find the probability ...
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What makes standard deviation a good measure of dispersion from the mean?

Standard deviation formula: If I just want to measure the amount of dispersion from the mean, why can't it be just an average of the absolute differences of each term from the mean? Something like ...
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Standard deviation on population vs sample

I have a problem in which I'm not sure whether to use the formula for standard deviation for a population, or standard deviation for a sample. The problem goes as follows: "Taxes: The increases of ...
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Is there a term for the (X - X BAR) section of the standard deviation formula?

That section I have highlighted - what is it called? I thought it may be called the "Mean Deviation" - but mean deviation implies that we are dealing with absolute values.
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How are standard deviations compounded over multiple periods?

I am using a simple compound interest formula to calculate the value of an investment over 18 years. I have access to the standard deviation of the investment, based on its asset allocations, which ...
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Error of standard deviation of a Bradley Terry model

I have a set of pairwise comparisons which I can fit the Bradley-Terry Model to. I am fitting it using a simple iterative algorithm according to Algorithm 1 of A Generalized Bradley-Terry Model: From ...
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How can I describe uniformity in a group of values?

I have a matrix of 128x128 (6384 numerical values) referring to light intensity. I will like to know how to calculate the uniformity of the values and I am currently using the standard deviation to ...
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Weighted probabilities assigned to a two stock portfolio

Does anyone know how to input a two variable portfolio with uneven weighted probabilties into an HP10bii+? By uneven I mean the weightings are not in increments of 10% and thus you can't simply equate ...
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Gaussian of different standard deviation and sample spacing

For given a set of samples position (e.g. $-2,-1,0,1,2$) I can define the correspondent, normalized, gaussian weights for a gaussian with std. deviation $1.0$. I know that if I scale all the sample ...
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Average and Standard Deviation for Angular Values

I'm trying to characterize an inexpensive accelerometer that provides (roll, pitch, yaw) values by generating basic running statistics (mean and standard deviation). But I'm unfamiliar with ...
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Variance reduction factor using gaussian filtering

I am currently trying to find the variance reduction ratio using gaussian filtering. For a simpler filter (as mean filtering for example), I am able to calculate it easily to find the well known ...