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 and alternate measures

Standard deviation is defined by $<(a - <a>)^2>$ for a continuous variable $a$. Does the term $<|a - <a>|>$ contain the exactly the same information. Is there a one-to-one ...
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Adding the averages and standard deviations of different sets correctly

I have $12$ balls with mean weight of $500$g, and S.D $25$g. I have $5$ balls with mean weight $200$g and S.D $10$g. If I combine all of them, is the mean just $8000\over17$ i.e. $$8000=500\cdot12+200\...
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Odds to probability - include field size and market dominance

I am trying to understand the conversion of odds to probability. Reading on the internet there seems to be many references to calculations like this. Horse Odds* Probability (from odds) ...
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Method of standardization of essay grades from a number of graders

Basically, there is a group of us grading a few hundred essays. We divided the number up so each of us grade 50, assigning a score 0-100 given a rubric. However, there is still subjectivity in the ...
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Error propagation: add errors in quadrature, or use a weighted standard deviation?

I have a measurement $x$ with a known uncertainty $\sigma_m$. I have a black box that can take an error-free measurement $x$ and produce a value $y$ with a known uncertainty $\sigma_{b}$ (which is ...
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140 views

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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Standard error of the estimate

Question: In order to estimate the total weight of rice of 100 bags, a sample of 25 bags was weighted, giving the average weight of 50 kg. If the population standard deviation is 1.5 kg, estimate the ...
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33 views

Finding the maximum number of students who made a certain score

In a class of 100 students, the mean score of the exam is 75, with a standard deviation of 6. What is the maximum number of students who could have made 100 on the exams? What I tried $P(X = 100) = ...
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Gaussian Smoothing Kernel Sigma from x-axis

I already asked a question and got great swift answers: Gaussian smoothing kernel with different sigma values However I have come across another problem. As I understand it, Gaussian kernels used ...
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21 views

Normalization of standard deviation

I have a question regarding standard deviation. Let me start with an example: I have response times (RT) from users, let's say RT1 = 3s RT2 = 5s RT3 = 8s I have ...
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Explaining the standard deviation formula

I'm revisiting standard deviation for the first time years, and i can't for the life of me recall the difference between two formulas. In particular, im also looking for how we arrived at these ...
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Confirmation of the Variance and Standard Deviation result

The following example is about Variance and Standard Deviation copied from Table 6.1 in the book "The Statistical Analysis of Experimental Data" by J Mandel. The Variance given is 667e-8 and ...
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Standard error of estimate

The question is : In order to estimate the total weight of 100 bags, a sample of 25 bags was weighted, giving the average weight of 50 kg. If the population standard deviation is 1.5 kg, estimate the ...
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How do I calculated a weighted standard deviation for a data set over several years?

I am trying to calculate the standard deviation for the following data set, 2010-2015: 2010: Mean=172.2 StDev=43.2 N=39 WtgMean=29.5 2011: Mean=165.1 StDev=36.9 N=27 WtgMean=19.6 2012: Mean=173.2 ...
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Given mean and standard deviation of the number of accidents in Town A, find mean and variance in Town B.

I'm having some trouble figuring out this question: The number of car accidents in Town A has mean $2.3$ car accidents per hour with standard deviation of $1.5$ car accidents per hour. It is ...
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53 views

Find probability that a newborn weighs between $6$ and $8$ pounds; given mean and standard deviation but not given sample size

The weight of a newborn baby randomly sampled from a particular population of babies is known to be normally distributed with a population mean weight of $7.25$ pounds and a population standard ...
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How to calculate sample variance?

I have an infinite population. Out of this population, I'm picking $N=40$ items, each of which can have a value of $0$ or $1$. Say I get a mean of $0.7$. How do I calculate the standard error of this ...
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error on the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as $1....
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Recalculate Standard Deviation

I know how to calculate a standard deviation when given a set of values. You must calculate the mean, then square the difference of each value between the mean to get the variance. Lastly, the ...
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51 views

Root mean square distance explanation

We know that $D_{rms}=\sqrt N$ where $N$ is the number of steps taken by the random walker. Now,consider a situation where a random walker walks $2$ steps in positive direction in the first two ...
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what is the unit of the following standardization formula?

If normalization would be to rescale the range of values to scale between $0$ and $1$ as follow: $x^{'}=\frac{x-\min(x)}{\max(x)-\min(x)}$ where the interval of $x^{'}$ is closed between $[0,1]$ ...
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Mean and standard deviation after a coin is tossed

Could someone help solve this? Let X equal the number of heads when $3600$ coins are tossed. Find the Mean and Standard Deviation of X
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Does a larger coefficient of variation mean larger variability?

I'm reviewing right now for an exam and I've stumbled across this online reviewer. In the solution for question #2 it stated that Section B is more consistent so there is greater variability in the ...
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How do you calculate the correlation between the intercept's and beta's standard error in a univariate linear regression?

I am running a regression to predict a variable Y as follows: $Y=\alpha+\beta\times x+\epsilon$ I am trying to get a distribution of the expected value of Y given standard errors in the model ...
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35 views

Standard deviation and standard error

I have a homework in which I am using data from NFL teams. This information was taken from the ESPN site and I was asked to calculate the following: $mean$, $standard$ $deviation$ and $standard$ $...
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SD probability problem involving chi-square distribution

Preparing for an exam in statistics, I have been pondering the following problem: Given that in country X 14 % of people hold a university degree, find the probability that for random sample of size ...
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According to Chebyshev's rule, how many observations should lie within one and a half standard deviations of the mean?

Using the formula : $p = 1 - k^{-2}$ I calculated that $p = 1 - 1.5^{-2} = 0.56$ , which equals to $56\%$. Because I have $24$ data points I go ahead and solve the number of points is $56\%$ of $24$:...
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54 views

Calculating the standard deviation involving a moment generating function

An actuary determines that the claim size for a certain class of accidents is a random variable, X, with moment generation function: $$M_X(t)=\frac{1}{(1-2500t)^4}.$$ Calculate the standard deviation ...
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75 views

What do I plug in for the z score?

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The ...
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How do I find the $Z$ value and calculate the $P$?

Please DO NOT answer the question, as I just need the right formulas in the form of plugging the numbers from the word problem into it. I struggle with this. And I need to find what the percentage is ...
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104 views

Ratios of median/mean and standard deviation/IQR in a normal distribution

I have some queries on the following question For a normal distribution, find the ratios of: (a) $\frac {\mbox{median}}{\mbox{mean}}$ (b) $\frac {\mbox{standard deviation}}{\mbox{interquartile ...
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Normal Distribution, percent less than mean minus one std. dev

GRE Question, part b. My answer is 16%, but the book says 15%. Why? mean = 65 cm stdev = 5 cm Probability that penguin chosen at random will be less than 60 cm is 16%, it shows in Normal ...
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Determine the standard deviation for statistical hypothesis testing when not explicitly given

I have got a video in grayscale, and I am interested to find out if the intensity of a pixel at a given location is more or less constant over time. I have been told here that I can use linear ...
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Standard Deviation vs Population Standard Deviation

In GRE study guide, it gives difference between standard deviation and sample or population standard deviation. I understand the mechanics of this, i.e. in standard deviation you divide all ...
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Normalize a list of standard deviations

I have several columns of features that I need to normalize to values between 0 and 1 (or -1 and 1, etc.--just something standard) in order to do regressions using ML algorithms (such as SVR, KNN, etc....
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Is it valid to calculate standard deviation for n=2?

My colleagues and I are having discussion whether it's valid to calculate standard deviation for $n=2$ or not? I think it's valid since I can calculate based on the equation, but higher N will give ...
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Standard deviation problem for short cut technique

Revised-GRE QUESTION I know how to evaluate the standard deviation and mean and also I have basic knowledge about the bell curve. But whenever I have to solve some problems related standard ...
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Mean of the deviations from the mean

I ve been struggling to understand the below problem.If I could get help with this problem, it would be greatly appreciated. Consider the data y, y+a, y+2a,….,y+na and the deviations of these ...
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Standard deviation without square

For $(x_i)_{1 \leq i \leq N}$, the standard deviation is of course $$\sigma = \sqrt{\frac{1}{N} \sum_i (x_i - m)^2},$$ where $m$ is the mean value of the $(x_i)$. We can say that the variance $\...
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How can the standard deviation be interpreted when the range is partially impossible?

After meassuring the answer time of a software system I calculated the standard deviation from the samples. The average time is about 200ms, the standard deviation $$\sigma = 300ms$$ According to the ...
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Using Minitab to compute an upper confidence bound for std deviation.

I've got a set of data and I want to answer the following: ...
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Specific confidence intervals question

As of now, I completely suck at computing confidence intervals, and I have an exam in a couple of days. The exact question is as follows: Some people are trying to measure a certain parameter $\...
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Why the standard deviation of the sample mean is calculated as $\frac{\sigma}{\sqrt{n}}$?

According to Wikipedia, the standard deviation of a sample mean is calculated as follows $$\frac{\sigma}{\sqrt{n}}$$ Why is that? Why do we need to divide the standard deviation of the population by ...
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Formula for standard deviation

So I am studying for a final exam and I know, or thought I knew, the formula for standard deviation. I quadruple checked in my notes and the slides for the lecture and see that the formula for the ...
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Did I equate the standard deviation correctly?

This was for a frequency table, so I will start from finding the mid points. For standard deviation, find the squares of the midpoints then multiply them by the frequency 7500.5², 12500.5², 17500.5², ...
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Is there a lower bound to the standard deviation of a Gaussian (Normal) distribution?

A Gaussian or Normal distribution is defined by the probability density function $$ f(x \; | \; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} } $$ with $\sigma$ as ...
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Standard Loss Function L(z)

z is the standard normal distribution F(z) is the probability normal distribution L(z) is the standard loss function i can find these values using below code in the excel z=NORMSINV(x) F(z)=NORMDIST(...
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Finding the variance of a group data set

Okay, so this is what I have so far for the means of these numbers. At this point I've added so many numbers together that my calculations are getting messed up. I need to know how to find the ...
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How do I find the variance for a group data set?

Okay, so this is what I have so far for the means of these numbers. At this point I've added so many numbers together that my calculations are getting messed up. I need to know how to find the ...