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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Why is the expected value of the squared value equal to the sum of the standard deviation and the mean?

I am currently reading the proof here that one has to divide by $n-1$ in order to get an unbiased estimator of the population variance. What I do not get is this: \begin{equation}E[y_i^2] = \sigma^2 ...
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standard deviation of a rate of phone calls

I am trying to implement some real time monitoring. I have a real time data feed from which I can calculate the number of phone calls received in the last hour (now-60 minutes). I want to alert when ...
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Why is my sample standard deviation not an unbiased estimator?

I was goofing around with a spreadsheet and decided to show empirically that the sample standard deviation is an unbiased estimator of the true population standard deviation. Link to Excel File I ...
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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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58 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, ...
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Writing a deviation from optimal formula

I really dont know how to write it as a proper mathematical formula instead of text, could you please help? Basically I have two formulas and apparently I they are not Mathematical.. Formula ...
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Standard Deviation Question

My working out: Median = mean = 60 Q3 = 25% of values at 75 25% = 0.25 = z-score of 0.68 Sx = (75-60)/0.68 = 22.3881 approx = 20... I said D The correct answer is B. 10
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Weighted mean from a set of average and standard deviation pairs

I'm trying to replicate some math a professor did related to Twitter sentiment analysis. Basically, there is a sentiment dictionary, called ANEW, that contains a mean and standard deviation for 3 ...
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Standard Deviation for Normally Distributed Bell Curve - Worded Problem

My working out: Z = (14-9.5)/2.25 = 2 % less than 2 = 95% Answer is 97.5 % .... no idea...
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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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Summing up Standard Deviations - best approximation

For a long data series the overall Standard Deviation shall be collected. However, due to memory constraints the data has to be aggregated per day - in a way that only one number is stored per day ...
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Given Standard Deviation and Population size, how can I calculate the number of population at mean

As per the title, I'd like to calculate the number of the population at mean, given a std.dev and population size. The use case for this, is Mobile Phone push notifications. I send the notification ...
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standard deviation of residuals: PCR vs MLR

Does anyone know, why the standard deviation of the residuals of a PCR (principal component regression) is greater than the one of a "normal" MLR (multivariate linear regression)? Thanks!
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How to answer probability question with basic std dev statistics

I have a data sample, say: $69$, $72$, $100$, $87$, $57$, $123$, $110$. Knowing the standard deviation and the mean what is the answer to the question: What is the number ($x$) for which $n\%$ out ...
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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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34 views

Standard deviation: When to use which sum-coefficient?

I'm wondering when to use $\sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ and when to use $\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ which I have both seen in ...
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50 views

How is the Standard Error and the Unbiased Estimate of the Variance Related?

I am going through a statistics textbook and there are two similar formula's that I cannot seem to grasp, one under the "Sampling Error" section and the other under the "Unbiased Estimator" section. ...
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Find the variance of $x$ when the standard deviation is given in the form of $ax+b$.

The standard deviation of $3x+7$ is $4$; then what is the variance of $x$? I know that variance is the square of the standard deviation but how does $3x+7$ and $x$ relate?
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Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
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can STD of subsets be used to arrive at the STD of the whole set

Assuming I have a set of values called S and the STD of S is Xs. Let's say I split S into two subsets S1 and S2 with standard deviations X1 and X2. The number of elements in S1 and S2 are called W1 ...
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32 views

The rule of the 3 sigmas -— how many times multiply the sigma to get 85%?

$\sigma c=\sqrt{\overline{R}(\sigma S)^{2}+\overline{S^{2}}(\sigma R^{2})}$ where, $\sigma c$ --- the buffer stock --- needed for maintaining the risk of stockouts, is used by logistitians ...
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29 views

Confidence interval and normal distribution

For question (a), is the answer 0.7143? For question (b), is the answer 10.85 and 11.95 ?
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I need a probability statement

I need some help with this question please. Make a probability statement about a group of workers who produced product data with a mean of 20 and a standard deviation of 1.03.
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Standard Deviation: Can I remove some data?

Suppose That I have measured property "X" in 16 points of a rigid body. This rigid body is consisted of two different materials. In one of them, property X is around 1, and in the other X is around 5. ...
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Normalizing data to a given value.

I would like compare the data by normalizing it to a given value. for example: [20,30,40,50,60,70] How do I normalize the given set of elements to its first value, ...
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mean and standard deviation of students taking a test

6 percent of all students of a class will not pass a test. There are 450 students taking this test. Let X represent the number, out of 450 students, who will pass this test. Find the mean and standard ...
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Solving Probability using standard Deviation and Mean

Given a normal random variable with mean 90 and a standard deviation 3, find the probability that x is greater than or equal to 86.67 and less than or equal to 96.33
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Exclude an RGB color from a set

I'm currently implementing an algorithm to split an image into smaller chunks, based on straight line separators. Here's the image I'm processing. It's very small, so you may want to save it and ...
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Calculation the Standard Deviation

I want to calculate the standard deviation of the following numbers: 30, 45, 45, 60, 75, 80, 90, 100, 110, 120. As far as I know, that would be ...
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67 views

Finding the variance of a normally-distributed random variable

X is a normally-distributed random variable, and $P[X<20] = 1/10 = P[X>100]$ I am trying to solve for the mean and the variance. I know that $\mu=60$ by symmetry. How can I solve for ...
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Convert list of test results into a comparative score

My students have completed a touch typing test that have given them a WPM (words per minute) result. I now want to give a score to those results out of an arbitrary number, say 10. I will later use ...
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Average of several harmonic means

I would like to know if it is possible to calculate the mean and the standard deviation for several harmonic means. More specifically, I have 20 harmonic means. And every harmonic mean was calculated ...
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125 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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Probability for Rolling 10 tethedrons 100 times

I am pretty confused about how to form the probability distribution function of the following question: Suppose you have a tetrahedron with numbers 1,2,3,4 on respective faces. If you roll 10 such ...
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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 ...
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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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133 views

Stuck…please help to understand how formula works in order to Find the standard deviation in normal distributions

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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statistcs z-table standard deviation question…Please help.

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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Please help ! A bit confused…I need to figure out exactlty what the question is asking me to determine.

Suppose that over a certain period prices of stocks in the S&P 500 can be approximately modeled using the normal distribution with $\mu = \$40.35$ and a standard deviation of $\$8.97$. The data ...
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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 ...
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Finding Missing Observed Scores given standard deviation and mean

The question that i'm being asked it: the mean of 10 observed scores was 20 and the standard deviation if 6.0. the observed scores are {16,11,20,24,29,24,16,20,,} what are the two missing scores I ...
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confidence interval of binomial disribution using standard deviation

Just as the normal distribution has the 68–95–99.7 rule with 68% of the data within +- 1 standard deviation and so on, does the binomial distribution too has something like that. Or does its being a ...
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Relationship between expected and actual value

Consider a zoo with two animals: an elephant and a lion. The elephant's expected lifespan is $70$ years, but it lives to be $65$ years ($SD = 7$). Likewise, the lion's expected lifespan is $22$ years, ...
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standard deviation of binned sample

I have to calculate the rms size of some sample (let's say 1D for this case). When I only have limted resolution my rms value gets bigger. What's the name of this effect again? Is there a way to ...
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Probability question help

A company that sells annuities must base the annual payout on the distribution of the length of life of the participants in the plan. Suppose the distribution of male participants' lifetimes is ...
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Normal distribution probability calculations

The following normal distributions represent race finishing times for a group of swimmers (S1 to S6). For example, Swimmer 1 (S1) has a mean finishing time of 60 seconds with a standard deviation of ...
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Normal distribution with less Probability [closed]

How do I calculate with Excel's formula to answer the question: What is the probability for a student's point is less than 560 by using excel? I know how to ...
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I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need? I may not be using the correct terminology so here's a graph: Based on this, if you ...
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Standard deviation of less than one

How would I find the approximate percentage of values within a standard deviation of less than one on the normal model? Chebyshev's rule is only used when the standard deviation is greater than or ...
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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 ...