# 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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1 vote
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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 ...
1 vote
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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, ... 63 views

### 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 ...
28 views

### 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 ...
• 101
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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 ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ... 35 views

### 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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