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 sample deviation in one pass

We've learned this algorithm in class but I'm not sure I've fully understood the correctness of this approach. It is known as Welford's algorithm for the sum of squares, as described in: Welford, ...
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Set of numbers given, find mean and SD of the other

A set of eight numbers has mean 5 and SD 4. The number 21 and another integer n are added to the set. The standard deviation of the set is now 6. Find n and the mean of the set now.
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Normal distribution involving $\Phi(z)$ and standard deviation

The random variable X has normal distribution with mean $\mu$ and standard deviation $\sigma$. $\mathbb{P}(X>31)=0.2743$ and $\mathbb{P}(X<39)=0.9192$. Find $\mu$ and $\sigma$.
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What does it mean if the cumulative normal = 1?

What is the significance of cumulative normal = 1? I am trying to program a game, however I have inherited code from another programmer. He is using the cumulative norm. his code is outputting a ...
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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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What does it mean to divide by the standard deviation?

I'm trying to variance normalise an image, in order to do so, I subtract the mean from the pixel value, to have a 0 mean, and divide by the standard deviation, to have a unit variance, right ? but ...
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How can I compare two averages of imperfect measurements, with their std. deviations?

I have a process by which I measure the times it take to do something, (run some code), and this time varies, a lot. I'm trying to optimize this code, making small changes that sometimes have small ...
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191 views

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 ...
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Standard Deviation algorithm for small population size?

I need to calculate the standard deviation on the entire population. The population size is 7, but for others it may be between 5-14. I see a few variance algorithms listed on Wikipedia. What stdev ...
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Course Grade - Statistics Question

I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows: ...
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Variance over two periods with known variances?

If period 1 has variance v1 and period 2 has variance v2, what is the variance over period 1 and period 2? (period 1 and period 2 are the same length) I've done some manual calculations with random ...
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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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765 views

Standard deviation calculation not matching up

I was looking up how standard deviations work, and tried to do it by hand, but what I'm getting isn't matching up with what I have in SQL Server. My population is: 1,2,3,4,5,6,7,8,9. I end up with ...
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Effects of subtracting numbers in a set of random variables on their mean and standard deviation

This is a question about linear combinations of independent random variables. X and Y are independent random variables. $X$ has mean 2 and standard deviation 4. $Y$ has mean 3 and standard deviation ...
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Help with problem: Estimated Standard Deviation of Regression Equation (Simple Linear)

This is a practice problem. I've solved part (a). I have provided verified answers (from the published key) to all parts (a), (b) and & (c). I need help solving (b) and (c). Consider a simple ...
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Financial Calculator HP 10bII - Standard Deviation with Probability

I have a financial calculator and am trying to use it to calculate the standard deviation when probability is involved. For a standard deviation question say on the numbers $1$, $5$, $6$, $10$ ...
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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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Charting Histogram Averages and Standard Deviation

Pretty basic question I'm sure: I have a 100 histograms, they are all created from randomly sampling the same data 100 times. Now, I want to show the 'average histogram' with markers at +1 standard ...
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Standard deviation of a rate

I am trying to measure the throughput of a network. I collected sample transfer times for 1,000 trials, and then calculated the arithmetic mean and standard deviation for the data (e.g., mean = 0.2s, ...
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Trying to find a meaningful statistical indicator to reflect user interaction with a website

A given user can interact in multiple ways with a website. Let's simplify a bit and say say a user can: Post a message Comment a message "like" something on the website via Facebook (after that we ...
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How can I figure out a set of values that most of my population will hit 99% of the time?

I am not a math person, I'm trying to put together a spreadsheet in excel that takes the square footage for every property in a county as the only input. I want to then generate a list of square ...
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241 views

Calculating Percent Variance Of Dates?

I have this problem where I have a set of data. Each data point has two values: Value1: Birthday Value2: Height Now, the problem I am faced with involves ...
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How can I calculate the standard deviation knowing an event probability and a number of trials?

I'm writing a test for a probabilistic data structure that I've implemented. Since its probabilistic, its performance is different every time, and in particular, the performance varies much more ...
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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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249 views

math distribution of averages and distribution of standard deviation for comparison of bytes

Let me change my question: I have a sequence of 512 numbers (these 512 numbers can have a value between 0 and 255) (in computer mode these numbers can be between 00000000 and 11111111 (bits)). For ...
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Standard error of the mean for root mean square of data

If I have a distribution of data, X, representing N samples taken during one measurement, then the mean square of X is $\bar{X^2} = \langle X^2 \rangle$, the variance of $X^2$, $\mathrm{var}(X^2)$ is ...
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Calculating mean and standard deviation of very large sample sizes

I have about 3.5GB worth of data that I need to get statistics from, all split up into about 71MB files, with an (approximately) equal number of samples. From this data, I would like to gather mean ...
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Is this true: $\mathrm{Cov}(X,Y) = \sqrt{\mathrm{Var(X)}}\sqrt{\mathrm{Var}(Y)}$?

I just want to confirm whether this is correct or not: The covariance of $X$ and $Y$ is equal to the standard deviation of $X$ times the standard deviation of $Y$. or, in mathematical notation, ...
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Can't find Standard Deviation for Continuous Random Variable

Here is my homework problem. Again, sorry for the formatting: A continuous random variable X has a symmetric distribution with mean 18. A brilliant mathematician has estimated that the probability ...
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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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How to calculate the expected value $E(XY)$ with known $E(X)$, $E(Y)$ and $\sigma_{i}$?

I am trying to understand the value of $\bar{x_{1} x_{2}}+E(x_{1} x_{2})$. For all $i$, $E(x_{i})$ and $\sigma_{i}$ are given. Wikipedia gives the joint probability density function: $E(XY) = \int ...
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Calculate standard deviation of merged sets with limited information (full details inside)

I have: A1: {3, 5, 6} and A2: {3, 4, 6, 8} Avg A1: 4.(6) Std.Deviation A1: 1.247 Avg A2: 5.25 Std. Deviation A2: 1.92 Merging A1 and A2, we get A12: {3, 3, 4, 5, 6, 6, 8} Avg A12: 5 Std. ...
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Calculating the “jaggedness” of a distribution

I'm sure "jaggedness" isn't the right term to use here, so please correct me. I'm trying to quantify how jagged a distribution is. For example, this is moderately jagged: distribution #1 This is ...
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Chebyshev's theorem

OK, so here's the question (not my homework - which is line segments -_-) According to Chebyshev's theorem, how many standard deviations from the mean would make up the central 60% 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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Is it possible to calculate the standard deviation without the samples?

Imagine I had two sets of samples. The only information I have about them is their Size Average Standard deviation Is it possible to calculate the standard deviation of a third set that is ...
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Max of multistep Gaussian walk vs max of multiple single-step Gaussian walks

Is there a relation between the max of a Gaussian random walk of 10 steps vs the max of 10 Gaussian random walks? Specifics (in Mathematica notation): ...
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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) ...