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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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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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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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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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: Why divide by $(N-1)$ rather than $N$?

The forumlae for standard deviation seems to be the square root of the sum of the squared deviation from mean divided by $N-1$. Why isn't it simply the square root of the mean of the squared ...
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890 views

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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1answer
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How to determine if Standard Deviation is high/low

I have derived the following response time data for a performance test I am running: Min - 8sec Max - 284sec Average - 28sec Standard Deviation - 27sec What does the standard deviation say about the ...
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536 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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404 views

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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3answers
965 views

7.7 standard deviations away from the mean?

I'm confused. I have a problem where I have to find the probability that x is below the z value 7.7. My z table only goes to z values of 3.4. How do I calculate this? These are the hints my teacher ...
3
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169 views

Why the natural log is there in MLE?

Why do we use natural log for MLE?
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1answer
100 views

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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121 views

Question about an article by Nassim Nicholas Taleb about the problems with standard deviation.

The article by Nassim Nicholas Taleb says that using standard deviation is flawed and is poorly understood and mean absolute deviation should be used. Because this article is short, and I don't ...
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305 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 ...
3
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1answer
339 views

Finding probability 400 components last 5012 or less hours using standard deviation?

The lifetime of certain electronic components is a random variable with the expectation of 5000 hours and a standard deviation of 100 hours. What is the probability that the average lifetime of 400 ...
3
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262 views

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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1answer
20 views

Standard Deviation of a Magic Square

I'm not sure if this is the right stackexchange to post this question to, but I was just wondering if someone had the answer to an interesting observation I've made. I've written a program that ...
3
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1answer
87 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 ...
3
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1answer
120 views

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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211 views

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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Relation between standard deviation and mean in random processes

In a Poisson distribution the square of the standard deviation $\sigma$ is equal to mean $\mu$ ($\sigma^2=\mu$) and in a binomial distribution $\sigma ^2=\mu\,(1-p)$ (with $p$ the probability of ...
3
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1answer
70 views

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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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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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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4answers
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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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Is Standard Deviation the same as Entropy?

We know that standard deviation (SD) represents the level of dispersion of a distribution. Thus a distribution with only one value (e.g., 1,1,1,1) has SD equals to zero. Similarly, such a distribution ...
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Why square the result of $x_1 - \bar{x}$ in the standard deviation? [duplicate]

I don't understand the necessity of square the result of $x_1 - \bar{x}$ in $$\sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}}$$. In fact I don't understand even why is $N - 1$ on the denominator ...
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2answers
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Is it possible to calculate the mean and standard deviation from a median and quartiles?

Any advice would helpful. I understand that the reporting of median and quartiles for small samples is an indication of skewed data. If such is correct, then is it useless to try to work out the mean ...
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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 ...
2
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1answer
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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 ...
2
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1answer
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Prove one standard deviation lies on inflection points

Is my conjecture correct that one standard deviation lies on the inflection points of the normal distribution curve (of the probability density function)? How can it be proved using the standard ...
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Simple question on standard deviation and mean.

This question has kinda stumped me: For a data set, the mean is 5 and the standard deviation is 1. There are 10 values in the data set. Is the range of the data set bigger, smaller or equal to ...
2
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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 ...
2
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1answer
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What is difference between standard deviation and Z-score?

I have read several explanations of standard deviation and z-score, I know how to it calculate them but I am not sure what is differences betwen them. Can someone explain it to me? When is suitable ...
2
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1answer
123 views

Bounding the standard deviation of a bounded random variable

Suppose $X$ is a random variable (discrete or continuous) whose values lie in the segment $[0,1]$. Is it safe to say that the standard deviation of $X$ is between $0$ and $\frac{1}{2}$?
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How to interpret standard deviation of samples with different means?

Let be two samples collections A and B. Mean of the first is 5 and the second is 15. Standard deviation of the first is 2 and the second is 5. Can we conclude something even though the two datasets ...
2
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1answer
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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 ...
2
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23 views

Is the variation of the mean 0, and the variance of standard deviation just the variance?

Just trying to get some properties straight. Was looking at a problem online which reads: Let X be a random variable with mean μ and variance σ2. What is the variance of X/σ+10μ? The solution of ...
2
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1answer
61 views

Chebychev to get at least 90 %

Im am given a list of integers and asked to give the interval that contains at least 90 % of my values. Values : $62,56,72,83,66,77,62,71,50,58, 74,81,76,67,70,70,69,67,80,81, ...
2
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1answer
237 views

standard deviation calculation using covariance?

i require a formula to calculate the standard deviation using variances of three or more variables (lets call them a,b,c) and the covariances between them. To complicate matters more i only need a ...
2
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1answer
70 views

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 ...
2
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1answer
199 views

Hypothesis testing for Variance - choosing a null hypothesis.

A gun-like apparatus has recently been designed to replace needles in administering vaccines. The apparatus can be set to inject different amounts of the serum, but because of random ...
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significance test

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
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Finding variance from bell curve

Find variance from the graph given. I know the mean is 6 but I have no idea how to find the variance using this graph
2
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Adding stochastic variables random variables where one has time component

Based on GLS regression I have identified two random variables lets call them A & B ...
2
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1answer
88 views

Margin of error for quotient of two measurements

I need to find the total margin of error for calculating velocity, while I have margins of error for time and distance. Actually the margins are the same (as both measurements were based on GPS - but ...
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1answer
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I need help with this review question. Business Calculus/Statistics

The question is: The scores on a test have a mean of 100 and a standard deviation of 8. A personnel manager wishes to select the top 60% of applicants. Find the cutoff score. Assume the variable is ...
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52 views

Standard deviation and intervals

I'm working on some homework and I'm stuck on a question that is not making sense to me in terms of my answer. The question states: ...
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135 views

Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...