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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Estimate the true mean: given only measurements above a known threshold

I have a computer-generated logfile which shows events which took longer than a particular time threshold (say 1 second for the sake of argument): if I measure the mean of these measurements, it seems ...
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How do you determine the sample size of a normal distribution?

I am presented with the question: The photoresist thickness in semiconductor manufacturing has a mean of 10 micrometers and a standard deviation of 1 micrometer. Assume that the thickness is ...
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Calculate risk that occurs p% of a time

In a search of a way to calculate variance for risk management I found the following formula (n1, n2, n3 are data points): ...
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finding percentage with the mean and standard deviation

if the mean of body temperatures is 98.6 degrees F with a standard deviation of .6 degrees F.....what percentage of bodies would have a temperature which lies between 98.6 and 99.2?
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57 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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29 views

Equivalent standard error for different populations

So I have population A and population B. The demographics are similar (assumes that the true expected value is the same in both populations). Population B, however, is twice the size of population A, ...
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172 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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87 views

Normal distribution probability problem.

There are lots of salmon in a pond and their length (in centimeters) obeys normal distribution $N(70, 5.4^2)$. You and your friend go fishing and decide to continue fishing until both of you catch at ...
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Linear regression model in econometrics and error's variance/standard deviation

In econometrics, there is a one-dependent, one-independent-variable linear regression model that goes like: $b_0 + b_1x +\epsilon = y$ where $b_0$ and $b_1$ are to be constant, and $\epsilon$ is error ...
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Calculating the expected value and the standard deviation of the total profit.

Company sells 2 kind of cars, Lamborghinis and Ferraris, and the sales of the cars are independent. From every sold Lamborghini the company gets 10000 dollar profit and for every Ferrari the company ...
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208 views

Standard deviation: mathematical manipulation

I am learning about standard deviation. In the book I am reading it defines standard deviation as: $$\sigma^2 = E[(x - E[x])^2]$$ so far no problem. In then states "simple mathematical manipulation ...
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change in sampling results and sample size

I am working on a problem, I have an experiment that each sampling gives me a numerical result. I want to create once a baseline of results that will give me very meaningful results. after creating ...
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Interquartile Rang concept / Problem?

If a set of data consists of only the first ten positive mulitple of $5$, what is the interquartile range of the set ? I have tried to solve but my answer is wrong..
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632 views

Understanding weighted standard deviation

Here is the formula that I use for weighted standard deviation: http://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf. My question is: why do we care about the number of nonzero ...
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Standard error of importance sampling estimator

I am currently studying Monte Carlo simulation and more specifically independent, importance sampling. Consider the following context: Assume we have some posterior pdf ...
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75 views

Finding 'symmetrical range' from mean.

A machine used to make butter where its masses are normally distributed with mean m and standard deviation s.It is found that 5% from these butters are having mass more than 85g where else 10% are of ...
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Length of Gaussian distributed variables

Suppose I have a set of random variables $x_1,...,x_n$ s.t. $x_i\sim N(\bar{x}_i,\sigma_i^2)$. And I define a new variable $x=\sqrt{x_1^2+...+x_n^2}$, then will $x$ also be normally distributed? And ...
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How $\mathbb E[\bar\epsilon_{i.}-\bar\epsilon_{..}]=0$ ? $\mathbb E$ denotes expectation.

Statistical model for Complete Randomized design $y_{ij} = \mu + \tau_i + \epsilon_{ij}$ where, $i$ denotes treatment and $j$ denotes observation. $i=1,2,...,k\quad and \quad j=1,2,..., n_i$ ...
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42 views

How do I determine a standard deviation with the mean and range known?

How do I determine a Standard deviation with the mean and range known?
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Explanation for correlation coefficients and standard deviation rolling 3 dice

Roll in MATLAB 500 times threesome-dice (3 dice) and sum them.Find in addition: max and min in each sequence mean values of sum/min/max. deviations of sum/min/max. correlation ...
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Propagation of standard deviation for random variable with Markov Property

I have a discrete random variable, $X \in \{0,1,2,3\}$. Define the indicator function: $$ 1_{k}\left(x\right) = \begin{cases} 1, & \text{if $x=k$} \\ 0, & \text{otherwise} \\ \end{cases}$$ ...
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Need help with a standard deviation/physics issue

I'm writing a little script for my mentor (physics stuff) and he wants me to put in a calculator for the standard deviation and wants us to be able to manually type in the upper/lower limits to take ...
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Need help with derivation of conditional expectation

The following is taken from the book "Mathematical Statistics for Economics and Business": \begin{align*} E\left.\left( \left[ Y-h(x) \right]^2\ \right\vert\ x\right) =& E\left.\left( ...
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Compare standard deviation with out using the standard formula

I very well know that Standard Deviation is the measure of spread of the data. If the data has higher deviation from its means then it has higher standard deviation. What if the data has same mean ...
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Removing outliers with standard deviation - is it possible to end up with an empty dataset?

There is a fairly standard technique of removing outliers from a sample by using standard deviation. Specifically, the technique is - remove from the sample dataset any points that lie 1(or 2, or 3) ...
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Why calculating variance this way is wrong?

I'm conducting a set of computer simulations (of membrane). I sample a property (area, $a$) in the following manner: $ A = \sum _1^N a \\ S = \sum _1^N a^2 $ During my data analysis, I calculate ...
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73 views

Mean or standard deviation?

Which one of mean or standard deviation can used to solve the following problem? A light bulb is considered defective if it lasts less than 400 hours. The following claim is made: 'Brand A ...
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130 views

Find the standard deviation of $ \frac{\gamma}{\sqrt{2\pi\sigma}}\exp\left(-\frac{\gamma^2}{\sigma}\frac{(x-\mu)^2}{2}\right)$

Given $\frac{\gamma}{\sqrt{2\pi\sigma}}\exp\left(-\frac{\gamma^2}{\sigma}\frac{(x-\mu)^2}{2}\right)$ as a normal distribution PDF with mean $\mu$, I'd like to solve for the std deviation in terms ...
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Is population standard deviation useful in the computers era?

Sample standard deviation used to approximate the population standard deviation. I can imagine this was very handy when you were dealing with a large population in pre-computer era. Now thanks to ...
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Trying to understand the standard deviation's formula [duplicate]

I have just started learning standard deviation and I'm trying to understand the formula. $$ s = \sqrt{ \frac{\sum(x-\bar x)^2}{n-1} } $$ Can anyone explain to me the square (and square root) part? ...
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222 views

Composite Standard Deviations

Normally, in AP Stats we were taught that to find the standard deviation of a new set of data, for example: to compute $stdv(A - B)$, you say $$stdv(A - B) = \sqrt{\text{var}(A) + \text{var}(B)}$$ ...
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Data estimation based on progression

Given a data-set $x$ and $y$. x | y ------------------ 153,000 | 0.058848 332,641 | 0.36352 506,629 | 0.53 If $x$ being the number of database records ...
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Regression vs. Normal Distribution

I have to estimate something using historical data. Should I find the equation of the curve of best fit to estimate? Or use a confidence interval, standard deviation, and a z-score to calculate it? ...
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Estimating time

I have some data about a number of projects that have been categorized. For each project, I have the proportion of the total project length that was spent on testing. For each category, I have to ...
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Hypergeometric Distribution Probability (mean, variance, Std Deviation)

The distribution of the number of children per household for households receiving aid to dependent children (ADC) in a large eastern city is as follows: 5% of ADC households have one child, 35% of ADC ...
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Normal/Not normal vs Known/Unknown

I have this table: ...
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Means and standard deviations.

Given three independent random variables $X_k$, the means and standard deviations respectively are $X_1 = (A, X)$, $X_2 = (B, Y)$, $X_3 = (C,Z)$. (1)What is the mean of their sum? (2)What is the ...
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Calculate the new average using standard deviation?

This is for a programming exercise. I have: the last average value the last standard deviation the total number of values I need to be able to add a new value to my average without knowing the ...
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Central limit theorem - std dev away from mean

I was reading about the CLT and found something that I think people use interchangeably. On one hand I found that 68% of the means are 1 standard deviations from away and 95% are 2 std dev. On the ...
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standard deviation of a certain distribution

If I have a list of N outcomes of drawing a number from the set {-1\$,+1\$}, and I know that the probability of getting (in a single draw) (-1\$) is p, and probability of getting (in a single draw) ...
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to calculate standard deviation using mean and sample size [duplicate]

Given the mean as $1336$ and sample size as $24$, how to calculate standard deviation when the deviation scores and sample figures are unknown.
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Do data points outside standard deviation persist in data subsets?

I have a data set of dates and values that are being plotted. I create a simple trend line y=a+bx using linear regression, and then I create a 'trend channel' (I ...
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Quadratic and geometric average

I'd like to find the find the quadratic average and the geometric average. To do this I have these informations : The standart deviation, the arithmetic average and the number of values. I know the ...
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Merging standard deviation of two groups with duplicates

I am using Parallel Algorithm (http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm) to merge standard deviation of two groups Can we merge two groups if there are ...
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Underlying assumption of t-test and standard error

I am having a hard time explaining why my significance test based on randomization is different from a t-test. I have 20 different data points and I know each comes from a Gaussian distribution. I ...
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How can I mathematically show the similarity between these 3 plots?

I have 3 3D plots of field strength measured around an antenna. I want to calculate the mathematical similarity between the points of the field patterns. How can I do this? thanks
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585 views

Can a Covariance matrix have negative elements?

I have a $N \times N$ covariance matrix $C$ of a multivariate Normal distribution. Can any of the elements of the Covariance matrix $C$ be negative for a real-valued distributions ?
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Recursive formula for variance

I'd like to know how I can recursively (edit: iteratively) compute variance, so that I may calculate the standard deviation of a very large dataset in javascript. The input is a sorted array of ...
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Standard error and p-values

I am a scientist who is currently doing a BSc. I did some stats a few years ago but since haven't touched it. I'm not sure how to calculate p-values for my data. A bit of background is that I am ...
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Finding a percentile in Excel

I am writing a program using excel and I need to find the percentage of a number. I have a few sample numbers and their percentages. 2.3% - 5.013368 5.0% - 5.238858 10.0% - 5.480078 25.0% - ...