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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check normality/accuracy of number based on a set

We have a set of numbers which collected by sensor, sensor produces a number based on some interval, and we store it on the set. Some time the sensor fails and produces incorrect number, how we can ...
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Compare two set of data [closed]

I choose Mean and STD (and I'm able to extract anything else) of a numeral DataSet, AS a representation of its content; and now I observed a new record. how can I say How much this new record is ...
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Bounding variance of any partition of deterministic values

We have a set of atomic non ordered observations say A=(1,2,9,5,4,8,1). A partition of this set can be P(A)=((1,2,9,1),(5,4,8)). var(P(A))=((1+2+9+1-E(P(A)))square+(5+4+8-E(P(A)))square)/2 and ...
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What's an intuitive description of the meaning of standard deviation in a discrete uniform distribution?

Just starting out with distributions, so I'm looking for an every day explanation to help me understand. I've read that for a discrete uniform distribution, the standard deviation is a measure of the ...
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15 views

Monte Carlo simulations, accuracy of mean vs variance of answers

I am working on a Monte Carlo simulation where two inputs are being used, $N$ is the amount of simulations I use, and $M$ controls the detail of each simulation (specifically the amount of time step ...
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56 views

Standard deviation of a baised $d$-sided coin

I know that that standard deviation of a noisy bit (a biased coin with probability distribution $\{ p, 1-p \}$ ) is given by $$ \sigma = \sqrt{p(1-p)} $$ What is then a measure of the standard ...
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17 views

Comparing sample and population standard deviation

I want to compute the standard deviation of some data points that I obtain during four series of experiments. For the first three experiments that I have conducted, the number of data points that I ...
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33 views

Standard deviation used in confidence interval for mean

I am a novice to Confidence intervals. To figure out the confidence interval for mean, one could either use the $Z$ distribution or t distribution depending on the sample size and population standard ...
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14 views

Maximum variance given x values on an interval [a,b]

Thanks in advance for the help. I'm exploring a possible solution to a problem. In order to explore it, however, I need to find the maximum variance of a set of numbers on a given interval. For ...
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25 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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51 views

Why is sample variance divided by $n-1$ and not $n$ [duplicate]

Sample Variance, customarily denoted, $s^2$, as in the formula below, is the average of the squared deviations, except that we divide by $n-1$ instead of $n$. $$s^2 = \frac{1}{n-1} ...
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Standard Deviation of Binomial vs Sampling Distribution

High school dropouts make up 14.1% of all Americans aged 18 to 24. A vocational school that wants to attract dropouts mails an advertising flyer to 25,000 persons between the ages of 18 and 24. (a) If ...
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49 views

Proof of Efron-Stein inequality

I was going through the proof of Efron-Stein inequality in this paper (page 219). I was unable to understand the following step $$\mathbb E\left[V_j \mathbb E\left[V_i|X_1,...,X_j\right]\right] = 0 ...
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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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29 views

Find the radius of a cluster, given that its center is the average of the centers of two other clusters

I do not know if it is possible to find it, but I am using Kmeans clustering with Mahout, and I am stuck to the following. In my implementation, I create with two different threads the following ...
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1answer
27 views

Comparing standard deviations of two unknown lists

Consider the following problem: List A contains 15 numbers in the range from 10 to 50. List B contains 15 numbers in the range from -50 to -10. Or any other two lists. Is there some trick to ...
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2answers
25 views

Standard deviation question - how did they get this answer!? so confused!?

Odwalla’s OJ is packaged in $250$ ml bottles and has a process standard deviation of $10$ ml. In monitoring the fill process, $6$ samples (of $25$ bottles each) were collected and averaged: $249$ ...
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Standard deviation of $Z = 9 - 3Y^3$

If Y is a random variable with probability mass function: Y | Pr(Y = y) -1 | 0.4 0 | 0.5 1 | 0.1 I need to find the standard deviation of $Z = 9 - 3Y^3$. ...
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1answer
19 views

How to estimate the variance of several populations when every population mean and variance is different?

I'm currently using the Pooled Variance method, but in my case I cannot assume that every population variance is the same. Is there a method for these cases ?
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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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Does the value of a standard deviation have any meaning [duplicate]

I understand that the standard deviation corresponds deviance from the mean but does the actual value of the standard deviation have any direct meaning? For example if you have a $\sigma$ of 10, does ...
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Is there any algorithm to divide the number list in multiple ranges?

(Moving question from stackoverflow) SOLR do not calculate ranges on numeric facets. We have to give the ranges while querying so that SOLR gives us the count at each range. But we cannot guess the ...
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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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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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87 views

fantasy basketball model

i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team ...
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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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Distribution of sample variance from normal distribution

Assuming $N$ samples $\{x_1,...,x_N\}$ are taken from a normal distribution with mean $\mu$ and variance $\sigma^2$, then the variance can be estimated using \begin{equation} ...
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probability of waiting time, chosen a random sample

The amount of time that a customer spends waiting in a counter is a random variable X with mean 8.2 minutes and SD = 1.5 minutes. A random sample of n = 81 customers is observed. Find the probability ...
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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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58 views

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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35 views

how to calculate standard deviation

I have the following chart. How do I calculate the standard deviation? I've tried to do that: $x=$ $[2^2*30+6^2*35+(9.5)^2*10+13.5^2*20+18^2*5)] \over 100 $ $-(7.25)^2$= 22.912 -> wrong answer. what ...
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Generating a data set that approximates another given random variable

One of the question my friend was asked in technical interview : The probability density function for a normal random variable with μ = 0.6 and σ = 0.7:​ Below is the code to generate the ...
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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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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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37 views

Standard Error in OLS Regression

Assuming I have the following linear regression set-up: $y_i = \alpha + x_i * \beta + \epsilon_i$ for $i = 1,2,..., n$. When I run the regession, I get a $\beta$ and $\alpha$ estimates, along ...
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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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rewriting formula containing covariance and variances

just trying to follow a formula. the equation starts of as follows, 1 = sum( xi * (cov(ri, r) / sigma^2(r) ) please note i's are subscripts then next line ...
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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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Is there a measure of 'evenness' of dispersion?

I looked up on the web, but couldn't find anything helpful. I'm basically looking for a way to measure how 'evenly' a value is distributed. As in, an 'evenly' distributed distribution like X: and ...
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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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1answer
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statistic normal distribution

Transport Canada was investigating accident records to find out how far from their residence people were 2 when they got into a traffic accident. They took the population of accident records from ...
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Standard deviation…

I have this random variable $X = \{-1, 0, 1\}$ with uniform repartition $p(X = -1) = p(X = 0) = p(X = 1) = \frac{1}{3}$. Expected value is $$E[X] = \sum_{i\in\{-1,0,1\}} x_ip_i = 0$$ Then variance ...
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If $E(W) = \mu$ and $Var(W) = \sigma^2$

This is one of two HW problems that I'm positing that I have no clue how to go about. If $E(W) = \mu$ and $\operatorname{Var}(W) = \sigma^2$ show that $E\left(\frac{W - \mu}{\sigma}\right) = 0$ and ...
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Is it possible to calculate standard deviation if I have sum of squares and number of samples as input?

I have following inputs Sum of the squares of the numbers. For example if the numbers are 1,4,6 the sum of squares is 53 (sq(1)+sq(4)+sq(6)). And I have the number of input samples: 3 in this ...
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Probability Between Two Normally Distributed Variables

The weight of medium-size tomatoes selected at random from a bin at the local supermarket is a normal random variable with mean $μ = 10$ ounces and standard deviation $σ = 1$ ounce. Suppose we pick ...
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Compute the Std. Deviation of Multiple Monte Carlo Estimation of $\pi$

For a school programming assignment, I am trying to compute the value of $\pi$ via the classic Monte Carlo estimation of $\pi$. In the experiment, we throw a variable number of darts at a circle that ...
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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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1answer
107 views

Analysis of IQ scores given mean, median, sd, quartiles

The statistics below provides a summary of IQ scores of 100 children Mean: 100 Median: 102 Standard Deviation: 10 First Quartile: 84 Third Quartile: 110 About 50 of the children in this sample have ...
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Probability that two points (any where on the curve) are a set number of standard deviations apart on a normal distribution

So, here is the question: You buy two pieces of pipe from supplier A, and the inner diameter has a normal distribution of N(muA, sigmaA^2) = N(8.02, 0.1^2). You want these two pipes to butt together ...