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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Standard deviation of phase for a random phasor sum

I have a phasor sum $a e^{j \theta} = \frac{1}{\sqrt{N}} \sum_{k=1}^{N} \alpha_k e^{j \phi_k }$ where $\phi_k = [-\pi, \pi]$, the standard deviation $\sigma_{\phi}$ of the phase is known and the ...
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do I reject or fail to reject the null hypothesis [on hold]

Mean and Standard Deviation of Job Performance for General ASU Population: M = 79.82, SD = 7.25 Mean of Job Performance for ASU Employees that Work Near Windows: M = 93.42 State whether we should ...
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12 views

Question Regarding finding the mean and variance of a MGF function?

This question confused me at the end where it says a normal random variable. A breakdown of the answer would be great The Question states: The MGF for the (general) normal distribution is given by ...
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Is Residual Standard Error the same as Residual Standard Deviation?

R's output gives you the Residual Standard Error but I am asked for the Residual Standard Deviation. Are those numbers the same? Also, how would you interpret the residual standard deviation? Thanks
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1answer
24 views

Find Standard Deviation Away From the Mean

Word Problem: In one town, the number of pounds of sugar consumed per person per year has a mean of $8$ pounds and a standard deviation of $1.7$ pounds. Henry consumed $11$ pounds of sugar ...
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37 views

Probability and Standard Deviation Study Help

I am studying for a mid term that I have tomorrow with last years exam. I went through it and did as much as I could. These are the two questions I didn't get correct. The correct answers (given) are ...
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32 views

Statistics Problem? [closed]

In a test of 20 students the mean was found to be 60 with a standard deviation of 10.If the standard deviation of 19 students is equal to 2.5,find the marks scored by the remaining student?
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48 views

Math Expectations and Standard Deviations

Pizza Shop profits are $1, $3, and $2 for each sale of their small, medium and large pizzas, respectively. If these are the probability distributions Small Size: $1 - 0.40 Medium Size: $3 - 0.20 ...
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calculating a moving average rate for detecting an outbreak

I have a count for the number of occurences of a disease over a period of time. I want to set a threshold for detecting unusaul increase with a moving average. I am planning to use + 1,2,3 SD to set ...
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24 views

Use chebyshev inequality to find the probability $P[|X-E[X]| \ge k\sigma]$

 For an arbitrary random variable $X$, use the Chebyshev inequality to show that the probability that $X$ is more than $k$ standard deviations from its expected value $E[X]$ satisfies ...
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4 views

Error from bias and noise in a linear operator

There's a result $S$ that depends linearly on some forcing $F$: $S=\int dt' G(t-t')F(t')$ Let's say I need to predict $S$, but can't measure $F$ exactly. I have both bias and noise in my ...
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25 views

Weighted Averages For Grades. But, no score for the final yet. How can I calc?

10% for Participation 10% for Workbooks 10% for Quizzes 40% for Tests 30% for Final Test. Students are asking for their current grade but I thought since one column is blank (final test, not taken) I ...
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28 views

What is the probability of two things happening at the same time?

I am using the normal distribution for two events so there is a 34% chance of each event having one standard deviation above the mean. What is the probability of both events having one standard ...
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22 views

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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14 views

Biased estimator for the standard deviation

Question: If a distribution is equally likely to take the values 1 or 4, show that $s_{n-1} $ forms a biased estimator of sigma. I started this question by finding that: $E(X)$ = 2.5, $E(X^2)$ = ...
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3answers
45 views

Variance is the squared difference - why not to the 3, or 4 instead?

So there is this question about why variance is squared. And the answer seems to be "because we get to do groovy maths when it is squared". Ok, that's cool, I can dig. However, I'm sitting ...
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22 views

Definition of Standard Deviation

We note that given a probability distribution function $P$ over a space $U$ the expected value of a function of the elements in U: $$ E(f(x)) = \int_{U} f(x)P(x) $$ We thus consider the mean as the ...
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45 views

Proof for Standard Deviation Formula for a Binomial Distribution

I understand the concept of standard deviation as the square root of the square of the mean of each sample value - the mean of the sample values. Here is the mathematical representation (I've solved ...
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Question composition rules in standard deviation

Standard deviation is defined as following: $f(x) = (\frac{1}{n} \sum_{i=1}^nx_i^2-(\frac{1}{n} \sum_{i=1}^nx_i)^2)^{1/2}$ Obviously, $(.)^{1/2}$ is not convex, so can I say $f(x)$ is not ...
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39 views

Alternative Standard Deviation Calculations

I recently inherited some code that does bounds checking from a coworker no longer with the company. It has the following comment //Currently, we use 3 sigma(standard deviation) as upper bound, ...
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41 views

Standard deviation of a random variable sampled from normal distributions

I was struggling to come up with a best question title. Anyway here is my question: Suppose I have a vector $\vec{S}$ containing non-negative values, each serves as the standard deviation for a ...
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16 views

Probability and standard deviation

Office has 4 copying machine, random variable x measure how many are in use at particular time. $p(X=0) = 0.08$ $p(X=1) = 0.11$ $p(X=2) = 0.27$ $p(X=3) = 0.33$ what is $p(X=4)$? I found $p(X =4) = ...
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1answer
24 views

Finding Mean and Standard Deviation using Z-Scores [closed]

An OPP study on Highway 401 found that 90 percent of motorists drive at speeds greater than 100 km/h and only 5 percent of motorists drive at speeds less than 95 km/h. Assuming the speeds are ...
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56 views

Mean for seat allocation

There are a set of kids (let's say 30) asked to sit in a row of seats, leaving at least one empty seat between them until all seats are filled. At the end, how do I calculate mean of the fraction of ...
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23 views

Problem solving the standard deviation for a stochastic variable

Information: In a laboratory we have a vial of water that's being kept on 50 degrees Celsius. This is measured with the best thermometer in the world. The standard deviation on this thermometer is ...
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check normality/accuracy of number based on a set

We have a set of numbers which collected by sensor, sensor produces a number based on some interval, and we store it on the set. Some time the sensor fails and produces incorrect number, how we can ...
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7 views

Bounding variance of any partition of deterministic values

We have a set of atomic non ordered observations say A=(1,2,9,5,4,8,1). A partition of this set can be P(A)=((1,2,9,1),(5,4,8)). var(P(A))=((1+2+9+1-E(P(A)))square+(5+4+8-E(P(A)))square)/2 and ...
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28 views

What's an intuitive description of the meaning of standard deviation in a discrete uniform distribution?

Just starting out with distributions, so I'm looking for an every day explanation to help me understand. I've read that for a discrete uniform distribution, the standard deviation is a measure of the ...
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22 views

Monte Carlo simulations, accuracy of mean vs variance of answers

I am working on a Monte Carlo simulation where two inputs are being used, $N$ is the amount of simulations I use, and $M$ controls the detail of each simulation (specifically the amount of time step ...
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57 views

Standard deviation of a baised $d$-sided coin

I know that that standard deviation of a noisy bit (a biased coin with probability distribution $\{ p, 1-p \}$ ) is given by $$ \sigma = \sqrt{p(1-p)} $$ What is then a measure of the standard ...
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30 views

Comparing sample and population standard deviation

I want to compute the standard deviation of some data points that I obtain during four series of experiments. For the first three experiments that I have conducted, the number of data points that I ...
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41 views

Standard deviation used in confidence interval for mean

I am a novice to Confidence intervals. To figure out the confidence interval for mean, one could either use the $Z$ distribution or t distribution depending on the sample size and population standard ...
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Maximum variance given x values on an interval [a,b]

Thanks in advance for the help. I'm exploring a possible solution to a problem. In order to explore it, however, I need to find the maximum variance of a set of numbers on a given interval. For ...
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31 views

Problem understanding Standard Deviation calculation

For a given dataset wm_t, the example for calculating standard deviation of the "gain" column is represented as: ...
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3answers
55 views

Why is sample variance divided by $n-1$ and not $n$ [duplicate]

Sample Variance, customarily denoted, $s^2$, as in the formula below, is the average of the squared deviations, except that we divide by $n-1$ instead of $n$. $$s^2 = \frac{1}{n-1} ...
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Standard Deviation of Binomial vs Sampling Distribution

High school dropouts make up 14.1% of all Americans aged 18 to 24. A vocational school that wants to attract dropouts mails an advertising flyer to 25,000 persons between the ages of 18 and 24. (a) If ...
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49 views

Proof of Efron-Stein inequality

I was going through the proof of Efron-Stein inequality in this paper (page 219). I was unable to understand the following step $$\mathbb E\left[V_j \mathbb E\left[V_i|X_1,...,X_j\right]\right] = 0 ...
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Relationship between exterior power of representation and variance?

I was reading the question: Symmetric and exterior power of representation regarding how to determine the character of an exterior power of a representation from the original representation. One of ...
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Find the radius of a cluster, given that its center is the average of the centers of two other clusters

I do not know if it is possible to find it, but I am using Kmeans clustering with Mahout, and I am stuck to the following. In my implementation, I create with two different threads the following ...
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Comparing standard deviations of two unknown lists

Consider the following problem: List A contains 15 numbers in the range from 10 to 50. List B contains 15 numbers in the range from -50 to -10. Or any other two lists. Is there some trick to ...
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2answers
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Standard deviation question - how did they get this answer!? so confused!?

Odwalla’s OJ is packaged in $250$ ml bottles and has a process standard deviation of $10$ ml. In monitoring the fill process, $6$ samples (of $25$ bottles each) were collected and averaged: $249$ ...
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Standard deviation of $Z = 9 - 3Y^3$

If Y is a random variable with probability mass function: Y | Pr(Y = y) -1 | 0.4 0 | 0.5 1 | 0.1 I need to find the standard deviation of $Z = 9 - 3Y^3$. ...
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1answer
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How to estimate the variance of several populations when every population mean and variance is different?

I'm currently using the Pooled Variance method, but in my case I cannot assume that every population variance is the same. Is there a method for these cases ?
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Collection of values: Root mean-square?

I am currently developing a music recommander system using the Million Song Dataset. This dataset contains 1mio songs and around 50 attributes related to them (how hot it is, the tempo, the key, the ...
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Prove the expression for standard deviation

Problem Let $x$ be a variable assuming the values $i=1,2,\ldots,k$ with frequencies $f_i$ and let $F'_i$ be the corresponding cumulative frequencies of the greater-than type, while $F''_i$ are ...
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Does the value of a standard deviation have any meaning [duplicate]

I understand that the standard deviation corresponds deviance from the mean but does the actual value of the standard deviation have any direct meaning? For example if you have a $\sigma$ of 10, does ...
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Is there any algorithm to divide the number list in multiple ranges?

(Moving question from stackoverflow) SOLR do not calculate ranges on numeric facets. We have to give the ranges while querying so that SOLR gives us the count at each range. But we cannot guess the ...
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How to interpret Standard Residual Deviation?

have fitted regression lines for 200 data sets where each data set contains 40 data points.As a result of that now I have 200 Standard Residual Deviation values and need to interpret that results. How ...
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Standard Deviation of 2D vector data

Given a sample set of wind data (speed and direction parallel to the earth), I would like to identify the consistency of wind samples. Standard deviation comes to mind, but I don't know if it is ...
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126 views

fantasy basketball model

i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team ...