# 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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