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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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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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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explain how this confidence interval is correct [on hold]

An srs of $16$ households is selected in Houston and the number of remote controls is counted. we are interested in a $99\%$ confidence interval for the population mean number. In the sample, the mean ...
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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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Expected value of variance and variance of variance?

From a certain system dynamical system I am able to calculate the expected error $\mathbb{E}(e_k)$ and the variance $\sigma^2 = \operatorname{var}(e_k) = \mathbb{E}(e_k^2) - \mathbb{E}(e_k)^2$, as ...
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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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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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23 views

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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52 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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24 views

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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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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26 views

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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56 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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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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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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36 views

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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19 views

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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34 views

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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76 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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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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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 ...
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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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Help solving: Normal Distribution problem without using the table OR with a given std

For a recent history test, scores follow the normal distribution with a mean of 70 points. 80% of the students scored below 88 points. What is the standard deviation of the scores? I have done a lot ...
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What does the multiplication of standard deviation of two variables gives?

If we need to find the correlation between two variables it is given by the formula - co variance of two variables divided by the multiplication of Standard deviation of the two variables. My ...
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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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Understanding standard deviation

If the mean is 50 and the standard deviation is 10. I am told that this means that "most of my data" falls within 10 points of 50. So "most of my data" is between 40 and 60. But what does this ...
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How to find the mean variable of a normal distribution with a given probability and standard deviation?

We have a machine that produces µ g of pasta to be stored in their package, with a standard deviation of 20g. It follows a normal distribution. And we don't want it to produce more than the package's ...