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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Average Sum and Standard Deviation When There Can Not Exist Repetition?
Imagine there are six cards with values from 1 to 6. Three cards are chosen at random, each card having an equal probability of being chosen, and their values are added together.
What will the average ...
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How to derive an analogue of the covariance matrix for standard deviation?
The covariance matrix can be interpreted as a summarization of a whole dataset into a single matrix representing a quadratic form that computes the variance of that dataset in a certain direction. I ...
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Standard Deviation of 4 Game Series
A game played by B and K involves indepenent rounds. In each round if B wins they receive 1 dollar from K, if K wins they receive 2 dollars from B, and in the event of a draw no money is given. K ...
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Why the probability density function must have the mean and std as parameters?
Intuitively, as I understand it, you have data points, and you want to check how exactly are they distributed, and you don't know if it's normal distribution or not.
What you need to do (intuitively) ...
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Finding a sequence of numbers of fixed length spanning a...b with the lowest average squared difference of ratios between subsequent ones.
The context is a design of gears in a bike cassette. The problem:
Design n-cog cassette (n is usually 11 or 12) with set lowest and biggest cog size so the average squared difference of gear change ...
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Find what four numbers have a standard deviation of 50 plus another constraint.
The standard deviation of $\mathrm{n}$ numbers $x_1, x_2, x_3, \ldots \ldots ., x_n$, with mean $\mathrm{x}$ is equal to $\sqrt{\frac{s}{n}}$, where $\mathrm{S}$ is the sum of the squared differences, ...
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Does the mean minus standard deviation always lie in the distribution?
Does it given a mean $\mu$, standard deviation $\sigma$ and quantile $Q(x)$ of a distribution (for example $Q(.5)$ is the median).
Does $\mu - \sigma$ always lie in the continuous distribution?
or
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Pearson correlation coefficient - proof
Can someone prove this formula ?
standard_devn_second_time_series = sqrt((1 - correlation_coefficient ^ 2) * variance(first_time_series))
first_time_series is given and I need to calculate the ...
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How can variance be unknown if you know the standard deviation?
Task is to campare two samples, standard deviation is know, variance is unknown (std. deviation is square root from variance) - how is it possible?
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Finding MLE of standard deviation and asymptotic variance of the estimator
Variables $X_{1}, . . . , X_{n}$ - random sample from normal distribution, $N(0,\theta)$. There I need to find:
the MLE of standard deviation of $X_{1}$;
the asymptotic variance of the estimator we ...
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Updating the variance of a sliding window without using stored data
There is a very nice way to compute the variance of a moving window as detailed by Knuth and Cook and answered locally here, also on a blog here. The method requires you to make use of the data in the ...
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What is the standard deviation of the sum of random variables?
Let's say I have N segments, which I put together into one large segment. The length of the segments is a random variable with a Gaussian distribution, expectation "a" and standard deviation ...
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Probability of a random sample lying between the mean and one standard deviation?
Is this a correct way of calculating the probability $P$ of a randomly selected sample from a distribution lying between the mean $\mu$ and the mean + standard deviation $\mu + \sigma$? Let the ...
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$Z$ standard normal distribution
I'm stuck in a notation problem which I cannot clarify:
I have a text which says :
$x = \text{some constant}* Z\left(\frac{[S(t)-S(t-1)]}{\text{standard deviation of S}}\right)$
with $Z$ standard ...
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Can the variance of the sample variance be negative?
In this answer is shown that the variance of the sample variance is
$$
\text{Var}(S^2) = \frac{1}{n} \left(\mu_4 - \frac{n-3}{n-1}\sigma^4\right)
$$
where $\mu_4$ is the fourth central moment, ie $E[(...
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How can I solve the expected number of frog jumps problem?
A frog sits on the real number line at 0. It makes repeated jumps of random
distance forward. For every jump, the frog advances by a random amount,
drawn (independently) from the uniform distribution ...
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Standard deviation of a normally-distributed dependent variable in a two-variable distribution assuming some degree of linear correlation between them
I have two variables, stress and deformation, which have some degree of linear correlation. My objective is to find the distribution (mean and standard deviation) only of the deformation variable ...
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List of 3 integers that gives 'simple' standard deviation
Does anyone know a list of 3 integers that gives a 'simple' answer when you calculate the standard deviation? Ideally it would be an integer that is not too great. For example when I have the vector
$$...
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what did standard deviation tell us?
in my first course in Statistics when I took the measure of variation the first thing intoduced to me is :(The variance) which has this formula :
\begin{gather*} \sigma^2=\frac{1}{N}\sum_{i=1}^{n}(x_{...
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How do I normalize/standardize a data set to a certain set value (not average, not min, not max)?
I know the formulas for standardizing, normalizing, and mean normalizing (if we take the wikipedia's definition for these terms). What I want to do is to normalize to a set value. For example, if I ...
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Find the formulaic relationship between sample size and standard deviation in a 2-group sampling problem.
We have two groups, each composed of n elements. For example, when n = 3, imagine that group 1 consists of ["A","A","A"] and group 2 consists of ["B","B&...
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Computing std dev given rms and mean
Say I have the rms of a dataset with values $x_i$, which was calculated as
$$ rms = \sqrt{\frac{1}{N}\sum x_i^2} $$
and a mean that was calculated as
$$ \mu = \frac{\sum x_i}{N} $$
Given these two ...
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Understanding deviation and squared error
I'm wondering if set of numbers 1 can have a lower standard deviation and a lower variance than an other set of numbers 2 while having a higher mean squared error comparing to the other set 2?
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Name of a statistical dispersion searched
Suppose I have a data set $ x=\{x_1,\dots, x_n\} $. Then does the following statistical dispersion exist?
$$ \frac 1 n \sum_{i,j\in n} |x_i-x_j| $$
If not, why? It is independent of mean values, ...
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The implication of (a 5%) significance level with a t-distribution in order to conclude a real difference
There is this standard in much of social "sciences" to use a 5% significance level to determine a significant degree of difference between two samples. That is two standard deviations. It ...
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Generalization of mean and standard deviation [duplicate]
I remember from my student years that we could generalize mean and standard deviation in one formula. The formula defines a statistical characteristic over a positive natural number, called degree, ...
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Confusion about the import of the standard error
The standard error is defined: $$ SD(\bar{X}) = \frac{\sigma}{\sqrt{n}} $$ where $\sigma$ is the standard deviation of the population and $n$ is the sample size. In the book I'm reading, it seems to ...
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Combining Math and Reading Test Scores presented in standard deviation units from the mean (mean not given)
I am working with a large dataset for regression purposes and am attempting to predict test scores using various societal / demographic factors. There are two scores, math and reading, that I am ...
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True standard deviation of the means vs Standard deviation of the mean of a sample
I am bit confused about the two terms, True standard deviation of mean and Standard deviation of mean of a sample.
I read that, if the Population is normally distributed with mean miu and s.d sigma, ...
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How to check if I need a relative or absolute Standard Deviation value
I may have accidentally written standard deviation value in my title when I meant deviation value alone. That is, how much a value deviates from mean. I'm unsure if I should consider abosolute or ...
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Introduce variance and standard deviation in a elementary class as a game
I'm about to introduce variance and standard deviation in class. The class has little or no prior knowledge of mathematics. What is the best way to introduce these terms? Is there perhaps a group game ...
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Given lists X and Y, if (1) their means are the same, (2) their standard deviations are the same, and (3) equality-Cauchy-Schwarz holds.. then X=Y?
Given (non-negative) $x$ and $y$, where their length is the same (i.e., |x|=|y|): if (1) mean of $x$ and mean of $y$ are the same (i.e., $\overline{x}=\overline{y}$); (2) their standard deviations are ...
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Find Standard Deviation of Multilinear Regression
I have from some measurements a data set and want to fit some parameters with multilinear regression. So I have basically with a Matrix $A \in \mathbb{R}^{n \times m}$, $b\in \mathbb{R}^n$ solved
$$\...
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Standard deviation from a graph given mean (Inertial Measurement)
I am trying to prepare for an exam, and a sample question given has the following figure
Accelerometer data
with the following mean information
Mean Information
The questions asks asks me to calculate ...
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Given (non-negative) lists 'x' and 'y', if their means and their standard deviations are the same, does this imply 'x=y'? How can I (simply) prove it?
Let us take a list/vector x and another one y, both of them composed of non-negative integers; e.g., ...
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Data Analysis statistic questions
Suppose 30 students in a class are randomly selected. If their heartbeats have a standard
deviation of 4 beats per minute (BPM). Are there any evidences to suggest that the standard deviation of the ...
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Why im getting standard deviation is zero
I have 10 values and I'm trying to find the standard deviation of these numbers
I am trying to find the standard deviation in Matlab, I'm getting the standard deviation is
zero
here are my data ...
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Variability of the first and second derivative
Suppose I have a time series. I take the first and second derivatives of the time series over the course of the whole time. An example can be found here in the last figure.
Now that I have the ...
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If $z=x+y$ are three variables where $x$ and $y$ are independent, then how can we prove that $\sigma_z^2=\sigma_x^2+\sigma_y^2$? [duplicate]
I tried to prove it using discrete data standard deviation formula, but I end up with $\sigma _z^2=\sigma_x^2+\sigma_y^2+2\bigg(\frac{\sum{x_iy_i}}{n}-\mu_x\mu_y\bigg)$. I read some elementary ...
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Is standardization assuming constant standard deviation and thus normality?
I'm trying to confirm if my inference about the following is right:
"Whenever we standardize something, we use (and thus assume), a constant standard deviation and thus normality distribution to ...
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How to Find the probability for a normal distribution
It is known that the income of guests at an all-inclusive resort on the north coast is normally distributed with a standard deviation of $\$8000$.
Suppose a random sample of $50$ guests is taken:
a) ...
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Organizing data based on upper outliers
I have many data sets (each with normalized values between 0 and 1) that I must classify based on how much it wanders above the an expected value (say 0.7).
At first I thought about using IQR, but ...
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Mean +/- 1 standard deviation always have majority of the values?
Let us say that we have a random probability distribution and we know it's Mean and it's Standard Deviation.
My question is that,...
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Compute standard Top & Bottom deviation of a serie
Context
I manage a big software project and we have a lot of "tasks" to execute.
Imagine we have 400 tasks, and they are in one of the following status:
a) backlog (not started)
b) in ...
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Error function for a different standard deviation
On Wikipedia I found the definition of the error function
$$\text{erf}(z)=\frac{2}{\sqrt{\pi}}\int_0^z e^{-t^2} \, \text{d}t$$
for a normally distributed random variable $X$ with mean 0 and standard ...
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How to understand "The plot displays combinations of values between one standard deviation below and one standard deviation above the mean"
I came across the following in an article that confused me.
Figure 1 shows the heterogeneity of combinations of technological and product market overlap between the alliance partners in our dataset.
...
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Proving Central Limit Theorem
I need some help with proving the Central Limit Theorem. I understand that the distribution of the sample means should be approximately normal with a mean that is the same as the mean of the parent ...
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Find rotation matrix for multivariate Gaussian such that sum of standard deviations is minimized
I'm struggeling with a part of a proof.
Let $A = \mathcal{N}(\mu, \Sigma)$ be a $n-$variate Gaussian, and let $R$ be a $n \times n$ rotation matrix. We can rotate this distribution by the rotation ...
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Normal distribution, and the exponent -(x-u)^2, and rationale for why "normal distribution" curve is so particularly good
The "normal distribution" is often described as if it were one of the great wonders of the world, or something like that. I am unable to see why. I definitely agree things in the universe, ...
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Variance of n-dimension data
I have a set of points in 3d space (x,y,z), and I'd like an indicator of how spread out they are. I'm thinking of using variance, but I've only seen it used for 1d data.
I assume that I would ...
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