Questions tagged [standard-deviation]

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. Use this tag alongside (statistics).

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Measuring variation of mean and variance in time series

I don't get how the variation of mean and $\sigma$ are measured for instance in the following picture from here: The red line is the mean of the data which changes. It is said that the standard ...
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Standard Deviation: The average weight of a set X of 100 bags of rice is 90 pounds

a. A>B b. A<B c. A=B d. Not enough info. I chose D because 'normal distribution' is not written in the problem. Otherwise I would choose (b) because A = 42 and B > 48 (the different between -...
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Getting a probability curve (Central Limit Theorem)

in a game I play there's a chance to get a good item with 1/1000. After 3200 runs I only got 1. So how can I calculate how likely that is and I remember there are graphs which have 1 sigma and 2 sigma ...
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Calculations of descents and inversions of the human genome

I am reading Normal Approximations for Descents and Inversions of Permutations of Multisets by Mark Conger and D. Viswanath and I'd like to do similar calculation like in section 3. However, I am not ...
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what is the percentage of items included within one standard deviation [closed]

So I came across this problem while solving statistics and not sure on how to solve it, Determine the percentage of items included within one standard deviation on either side of the mean: Class ...
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Does adding a constant or reducing all the numbers by 5% change the z score?

I have a set of numbers. I have two cases: If I add a constant to them, does the mean, standard deviation and z score change? What I think: Mean changes, std deviation doesn't change and z score ...
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Standard Deviation of Character Gradients in a Document Image

I have the paper titled "CG-DIQA: No-reference Document Image Quality Assessment Based on Character Gradient". It is all about assessing the quality of the document image based on its ...
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How to define a trigonometric function, given standard deviation for x and y?

I would like to define a trigonometric function of the form $f(x)=\alpha \cos^2(P\pi x)$ where I can define $\alpha$ as an amplitude as the function's range, and $P$ as a period related the standard ...
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Rough rule of thumb for when to use $N$ and when to use $N-1$ when calculating variance.

I don't really understand the whole concept of estimators and biased/unbiased etc with regards to calculating the standard deviation. Is there a rough rule of thumb that I can use to know when I ...
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Why don't we just take the root of the numerator instead of taking the root of the whole thing in the expression for standard deviation?

The equation of the standard deviation of a dataset is given by $\sqrt{\frac{\sum{(x_{i} - \bar{x}})^2}{N}}$. Why is that the case and why can't we use $\frac{\sqrt{\sum{(x_{i} - \bar{x}})^2}}{N}$ ...
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What kind of deviation is the $sx$ button on my calculator?

I'm learning about standard deviation and I notice there is another kind of deviation option on my calculator. The standard deviation is denoted by $\sigma x$ on my calculator while the other kind of ...
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How to “denormalize” a standard deviation?

Lets say I have a vector of variables which have all been standard normalized with $(\mu_n, \sigma_n)$ by doing the operation $\frac{\mathbf{y} - \mu_n}{\sigma_n}$. I then have a model which predicts ...
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Get the weights of porfolio variance given standard deviation

I am trying to create a Simulated Portfolio Optimization based on Efficient Frontier on 50 stocks, which you can find the csv here. Yet it already takes me several minutes to get a suboptimal solution:...
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A machine is used to fill packets with rice. The contents of each packet weighs X grams - Normal Distribution

A machine is used to fill packets with rice. The contents of each packet weighs X grams. X is normally distributed with mean μ grams and standard deviation 3.71 grams. The mean weight μ is stated to ...
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Measure of spread or amout of information in a standardized distribution (how to calculate entropy?)

Suppose I have a distribution of scores {-1, 0, 1} and another distribution of scores {-0.70711, 0.70711}. These two distributions have the same mean, 0, and almost the same standard deviation, ...
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Statistics on Lottery Data

I'm working on a project for school. So I have 3 years of historical lottery data that I'm supposed to describe the data make some inferences from it. Here's a short description of my data: There are ...
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Manhattan 5lb, Standard Deviation and Normal Distribution, Question 6 [closed]

the question image Set X consists of 9 total terms, but only two different terms. Six of the terms are each equal to twice the value of each of the remaining 3. Which of the following would provide ...
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Determine the vector that produces the biggest deviation

Given a set of points $a_i(x,y)$ in the 2-Dimensional plane how can I determine the unit vector $u$ which produces the biggest standard-deviation in the $<a_i,u>$ (scalar product) values? I ...
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Calculate confidence level from a given confidence interval

I'm fairly comfortable calculating the confidence interval. But now I'm seeing a problem where I'm giving a confidence interval $CI(27.6621, 30.3379)$ and I'm requested to calculate the confidence ...
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For standard deviation of grouped data shouldn't you have to convert frequencies given in decimals (in millions) to whole numbers.

A client of mine in Finite Math received the following data and was asked to find the sample standard deviation. (Actually, they don't specify 'sample'. This class doesn't seem to teach population ...
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Correctly Scaling the Standard Deviation in Scaled Measurements raised to a power

We're working on a project that plots flux density of a light curve with respect to time. To do this, we had to scale data from different wavelengths so we had just the one variable for the flux. ...
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Payout amount dependent upon value for each person in population

I am a software developer tasked with solving a problem programmatically, but I'm limited in what I remember about statistics and am not sure how to properly word my question to search for the answer. ...
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Why is the standard error used (instead of the standard deviation) when reporting the results of measurements made with scientific instruments?

One explanation that I was given is that you are considering the measurements you've made to be a sample from an infinite population of measurements that could be taken with that instrument under the ...
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Nice bounds for 3rd folded central moment in terms of variance?

Say we have some real numbers $x_1, \ldots, x_n$, and let $\mu$ be their mean and $\sigma^2$ be the variance. Are there some nice bounds for $\frac 1n \sum_{i=1}^n |x_i - \mu|^3$ based on $\sigma^2$? ...
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Query on the standard deviation formula

It is widely known that the variance formula is: $S^{2}=\frac{\sum_{i=1}^{n}\left ( X_{i} - \overline{X} \right )^{^{2}}}{n-1}$ and that the standard deviation formula is: $S^{2}=\sqrt[]{\frac{\...
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The relationship between expectation and standard deviation [closed]

Let $X$ be a real valued random variable with finite expectation $E(X)$ and standard deviation $D(X)$. Then $(D(X))^2\leq E(X^2)$ I started to think like following: $$D(X) = E(X^2) - (E(X))^2\\(D(X))^...
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How to measure the understanding level of a new concept that was taught to a group of students

Let us say I am an online teacher and I have to introduce a new topic in the class today. Let us say the topic is "Solving a Quadratic Equation". There is an online community of students from ...
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Proper way to calculate the mean of a dataset - use the entire dataset or the frequency table values?

I'm not trained in mathematics, but I took a course about using statistics in understanding hotel data. One step of the process requires us to calculate the mean rate of a collection of stay records. ...
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How 3rd Quartile (Q3) is positioned at 0.675 SD in case of normally distributed data?

How was the problem created? I was reading answer of this question where the author remarked that The 3rd quartile (Q3) is positioned at .675 SD (std deviation, sigma) for a normal distribution. ...
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Hello, why is it that the formula of Standard deviation (of both grouped and ungrouped data ) differs in different sources

For instance, the formula for standard deviation of UNGROUPED data in some books is $\sigma={\sqrt {\frac {\sum(x-{\bar X})^{2}}{n}}}$ while in some books, they subtract 1 from the n (number of items ...
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How to Calculate Statistics for Open-Ended Frequency Distribution

If you had a frequency distribution something like the below (and did not have the raw data), how would you calculate statistics without being able to determine the midpoint of the final range (595+). ...
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Help with finding a metric for tightness of experiment from probability of success

I'm an amateur with some interest in statistics and I would appreciate it if anyone could verify that I didn't make any mistakes on how I tried to tackle a specific problem I encountered, or give me ...
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Poisson Distribution with exponential probability. Finding the probability of falling between 1 and 2 SD of the mean

The number of customer arrivals at a bank's drive-up window in a 15 minute period is Poisson distributed with a mean of seven customer arrivals per 15-minute period. Define the random variable x to be ...
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Statistics question: how do I use standard deviation in this case? [closed]

$y$ is a function of $a, b$ and $c.$ I have data for a, b and c over a period of time. I am plotting a graph of $y$ against time. At the time $= t_{\text{lost}}$, I start to lose all $c$ values. ...
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Effect on variance when 2 observations out of the set of n observations are added and subtracted with a constant

Set $y$ is given such that, $$y= (y_1,y_2,...,y_n)$$ And $$y_1\leq y_2\leq...\leq y_n$$ Now take $y'$ such that $$y'= (y_1,\ y_2,...,\ y_j+c,\ y_{j +1},....,\ y_k-c,\ y_{k +1}...,y_n)$$ ...
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Best way to determine improvement knowing the mean, standard deviation and standard error of the measures

I have data of a study carried out on two groups of people, one of 13 and the other of 22. Each group was given two measurements, one at the start of the experiment and another one at the end. ...
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What does the “standard” in “standard deviation” mean?

I know what the standard deviation is. However, I can't make sense of its name. What does the word "standard" refer to? Is it a synonym for mean, so that the "standard deviation" is the "deviation ...
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Why is sample covariance divided by (n - 1) not (n - 2)?

Why is sample covariance divided by n - 1 and not n - 2? We have two statistics that are estimated, which are the two sample means of variables. Should that not mean we use up two degrees of freedom?...
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Linear Algebra Geometry Behind the Standard Deviation

The standard deviation of the sum of $m$ draws with replacement from an urn containing $n$ numbers (which I'll represent with the $n$-dimensional vecor $\vec v$) is given by the expression $sd(\vec v)√...
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Finding the mean and variance of new random variable, from three existing random variables

If R is the new random variable, derived from original random variable X, altered by two other random variables X and Y in the form of $$\ R = \sqrt{(X + A)^2 + B^2} $$ X is a normal random ...
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A squared integrals

Is it true that $$ \left(\int_{0}^{t}f(u)du\right)^{2}=\left(\int_{0}^{t}f(u)du\right)\cdot\left(\int_{0}^{t}f(v)dv\right)=\int_{0}^{t}\int_{0}^{t}f(u)f(v)dudv\;? $$ I have tried to prove it with ...
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Covariance of a random variable and its mean

I want to find the value of $cov(X, \bar{X})$. If I input this in the formula, I will get: $\sum (X - \bar{X})(\bar{X} - \bar{X})/N = 0 \:\:\:\:\:\:(\because \bar{\bar{X}} = \bar{X})$ Edit: Here $X$ ...
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Change of variables for normal distribution

I consider a normal distribution $f(x;\mu_x,\sigma_x)$ with mean $\mu_x = 190$ and standard deviation $\sigma_x =3.08$, which gives me the exemplary value of $f(x=200;\mu_x,\sigma_x) \sim 10^{-5}$. ...
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How do I find standard deviation in this problem?

In the ordered line : X: 4, 5, 9, 10, 11, 13, 16 P(X) 0.12, 0.1, 0.11,0.11,0.14,0.34,0,08 what is standard deviation? the mean is 10.31 Can you guys help me to find the standard ...
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Standard deviation, standard error and confidence interval difference explanation

I write some code to generate random weights (I define low as 50Kg and high as 100Kg) of males, then generate 100 samples containing 100 measurements (weights per sample) i.e. 100 samples and each ...
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Averaging Datasets with Inconsistent Time Points

I am trying to find the equivalent of a "mean" and "standard deviation" of some time-dependent datasets, with the added complication that not all datasets were taken at consistent time points. Say, ...
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What is the name of this statistical measurement?

We have a target value for $ x $ called $ x_t $, and we have the average value for $ x $ given as $ \overline x $. If we take the absolute value of the average minus the target we get a measure of how ...
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The difference between standard deviation $=0$ and no standard deviation [closed]

I would like to ask if there is the difference in the interpretation standard deviation of the Gaussian $=0$, and there is no standard deviation for the Gaussian. Is it the same? Or there is some ...
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Algebra standard deviation

The average math score on the SAT for Melon Valley High School is 500. The standard deviation is 25 points. If 300 students take the test how many students will score between 475 and 525? Question ...
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Looking for an explanation over a standard deviation formula in C#

I found the following standard deviation formula by Victor Chen in a stackoverflow thread. I'm trying to understand why he calculates it like this: ...

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