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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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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Calculating missing data points from standard deviation and mean

I have to figure out what to missing data points are from a set of 10 scores. The mean of the 10 observed scores is 20.0 and the standard deviation is 6.0. The observed scores are listed below, with ...
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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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Expected Value and Standard Deviation for sample

Randomly selecting 50 people from a population, 45% say 'YES' and 55% say 'NO'. Assuming that the true percentage of people in the population who say 'YES' is 48%, what is the expected value and ...
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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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343 views

Statistics Question: Revenue & Cost

Data for costs of production for a firm every month from January 2001 to December 2002. Data is denoted by $d_1, d_2,...,d_{24}$. The following info is calculated from the data set. Mean cost = ...
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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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Statistics - Z-score confusion.

For z score, you are taking the sample value subtracting population mean and dividing it by std deviation. Is that correct so far? Now, the "sample value" is defined by an equation. In my scenario, I ...
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476 views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
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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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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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Variance of a max function

Say $x_1$ and $x_2$ are normal random variables with known means and standard deviations and $C$ is a constant. If $y = \max(x_1,x_2,C)$, what is $\mathrm{Var}(y)$? Well, I forgot to tell that $x_1$ ...
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338 views

Weighted Standard Deviation for Histogram Bin Height

I'm plotting some binned data in the form of a histogram. Say I have 10 data points, each composed of a bin to be placed in, and then a "height". Then I might have something like: Bin Height 0 - ...
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Converting standard deviation number

This is math finance question. I'm trying to figure out the formula for converting the standard deviation of % changes in prices for a sample of days into the standard deviation of % changes in prices ...
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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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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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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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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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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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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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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 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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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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75 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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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 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 ...