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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Motivation behind standard deviation?

Let's take the numbers 0-10. Their mean is 5, and the individual deviations from 5 are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 And so the average (magnitude of) ...
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Sample Standard Deviation vs. Population Standard Deviation

I have an HP 50g graphing calculator and I am using it to calculate the standard deviation of some data. In the statistics calculation there is a type which can have two values: Sample Population I ...
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Why do statisticians like “$n-1$” instead of “$n$”?

Does anyone have an intuitive explanation (no formulas, just words! :D) about the "$n-1$" instead of "$n$" in the unbiased variance estimator $$S_n^2 = \dfrac{\sum\limits_{i = 1}^n ...
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Why is there not a simpler way to calculate the standard deviation?

Steps of getting standard deviation. http://www.techbookreport.com/tutorials/stddev-30-secs.html: Work out the average (mean value) of your set of numbers Work out the difference between each ...
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How can I calculate “most popular” more accurately?

I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ...
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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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Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are ...
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Generate a set of random numbers with a normal distribution

I am trying to generate a set of N random numbers where the set has a normal distribution. I'm currently using a brute force approach: Randomly select N numbers from a normal distribution. Check ...
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Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ...
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Central Limit Theorem: asymptotic distribution

I keep reading in the documents about the asymptotic distribution of the CLT. I am learning things by myself so try to figure it out on my own and don't have a teacher to ask the question to. So it's ...
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is it possible to calculate the standard deviation with a given mean and sample size?

I have been going in rounds with this problem... I may be thinking "complicated", any advice? I have the mean and total sample size (=number of data points) and I need to know what is the standard ...
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incremental computation of standard deviation

How can I compute the standard deviation in an incremental way (using the new value and the last computed mean and/or std deviation) ? for the non incremental way, I just do something like: ...
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Determining variance from sum of two random correlated variables

I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated? ...
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Standard deviation of the product of gaussians

What is the standard deviation of the product of two random variables that each have Gaussian Distributions? I don't even know where to begin on this problem.
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Continuously sampled event: Estimating the value of a future data point, based on past measurements and their tendency

Problem I'd appreciate some ideas on how to define a formula to estimate the value of a future data point for a continuously sampled event, based on past measurements and their tendency. At any ...
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Normal Distribution - What should I study to understand these questions [on hold]

I got these questions from someone. I am not expecting anyone to 'solve' these, just need an idea of which specific topics I should read up on to help the concerned person understand, as I have been ...
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Bootstrap method failing where blocking works

I'm computing an average of individual samples that are not entirely independent and need an estimate for the true standard deviation. According to Newman and Barkema's book the most reliable method ...
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Denominator to calculate standard deviation

I've just read something about calculating sample standard deviation. Some explanations say that it is because of degree of freedom. With a constraint that the mean should be zero, we do actually have ...
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When plotting a bell curve from an array of values, is it possible that +/- 2 standard deviations from the mean can fall outside the range of values?

First, this is not homework, it is actually for work. It's been a couple of years since I've done stats and need some help! I've googled for this problem but was unavailable to find any resources that ...
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Relation of mean of standard deviations and standard deviation

Let $\{x_{i,j} : i=1..7,j=1,..n\}$ be a set of samples from $n$ weeks (where $i$ denotes the day of the week). Is there any interesting information to be gleaned from the relationship (ratio, ...
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Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
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standard deviation find the probability that more than 30%

A manufacturer produces a certain type of components that has a length of $2.1 \,\mathrm{cm}$. the distribution of this components is normal with mean $2.15 \,\mathrm{cm}$ and sd $0.4 \,\mathrm{cm}$. ...
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Method for determining the average deviation of data values over time?

I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet. For convenience, I've set the minimum and maximum values on the y-axis to the weights that ...
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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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Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...
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variance reduction

Say i have $n$ variables with variances $V_1,V_2,...V_n$. The sum of the variables will have a variance of $V=V_1+V_2+..V_n$ .Now if i am given N total simulations to reduce the variance V, how do i ...
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Uniform distribution, Expected value and standard deviation for proportion of observations in a subintervall

$X\sim U(0,1)$. Divide the interval [0,1] into k equal subintervals. Then $X_1$=the number of observtions on the first interval. Define the new variable $Y_1=X_1/n$, where n is the number of ...
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Finding probability given mean and standard deviation

I don't know how to approach this problem: X is normally distributed with a mean of 200 and a standard deviation of 10. Find P(X ≥ 203)
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Fast way to recalculate average and standard deviation as new values arrive

Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...
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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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Normalising Standard Deviation as score for Burstiness calculation

I have measured the frequency of terms within the same period (say 14 days), and I wish to use Standard Deviation to calculate their burstiness (i.e. which terms are more spiky), therefore, if a term ...