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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2answers
25 views

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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1answer
919 views

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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1answer
385 views

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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1answer
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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504 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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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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1answer
355 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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1answer
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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1answer
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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361 views

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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1answer
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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1answer
347 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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3answers
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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19 views

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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1answer
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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1answer
523 views

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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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
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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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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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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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26 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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1answer
15 views

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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85 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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30 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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1answer
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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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1answer
30 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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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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1answer
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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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1answer
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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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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1answer
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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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2answers
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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 ...