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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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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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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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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Variance is the squared difference - why not to the 3, or 4 instead?

So there is this question about why variance is squared. And the answer seems to be "because we get to do groovy maths when it is squared". Ok, that's cool, I can dig. However, I'm sitting ...
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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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Proof for Standard Deviation Formula for a Binomial Distribution

I understand the concept of standard deviation as the square root of the square of the mean of each sample value - the mean of the sample values. Here is the mathematical representation (I've solved ...
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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 ...
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Alternative Standard Deviation Calculations

I recently inherited some code that does bounds checking from a coworker no longer with the company. It has the following comment //Currently, we use 3 sigma(standard deviation) as upper bound, ...
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Standard deviation of a random variable sampled from normal distributions

I was struggling to come up with a best question title. Anyway here is my question: Suppose I have a vector $\vec{S}$ containing non-negative values, each serves as the standard deviation for a ...
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Probability and standard deviation

Office has 4 copying machine, random variable x measure how many are in use at particular time. $p(X=0) = 0.08$ $p(X=1) = 0.11$ $p(X=2) = 0.27$ $p(X=3) = 0.33$ what is $p(X=4)$? I found $p(X =4) = ...
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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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Problem solving the standard deviation for a stochastic variable

Information: In a laboratory we have a vial of water that's being kept on 50 degrees Celsius. This is measured with the best thermometer in the world. The standard deviation on this thermometer is ...
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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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65 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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79 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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59 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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51 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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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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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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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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60 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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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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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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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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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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404 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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29 views

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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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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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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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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360 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 ...
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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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177 views

Finding variance and standard deviation of a random variable in an equation

Suppose that X is a random variable with mean 17 and standard deviation 5. Also suppose that Y is a random variable with mean 45 and standard deviation 11. Find the variance and standard deviation of ...
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Finding the mean of a random variable in an equation given standard deviation and mean

Please help! What do I plug into these equations to solve for the mean of Z?? Suppose that X is a random variable with mean 23 and standard deviation 5. Also suppose that Y is a random variable with ...