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### What is the expected value and the mean of sample standard deviation? [duplicate]

What is the expected value and the mean of sample standard deviation? I know that I can derive the expectation and variance of sample variance using the $\chi^2$ pdf. But I don't know how to start ...
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### Unbiased estimator of standard deviation of a normal distribution, using gamma function [duplicate]

According to the Wikipedia article, the following estimator of the standard deviation $$s=\sqrt{\frac{1}{n-1}\sum_{k=1}^n(x_i-\bar{x})^2}$$ for a normal variable, verifies $E[s]=C_4(n) \sigma$, where ...
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### The derivation of standard deviation [duplicate]

So, if there are $N$ data points in my sample space of any randomly distributed variable $X$. The standard deviation, $\sigma$, (from my understanding) is the root mean squared of the error (from the ...
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### Estimating process standard deviation for a quality control chart. What is $s/(c4)$ and how to calculate it in R? [duplicate]

I recently came across quality control charts in my studies and found out that the estimator $$\hat \sigma =\frac{s}{c_4}$$ is preferred for UCL and LCL calculations in an x-bar chart as it is ...
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### why is standard deviation a biased estimator [duplicate]

In this post: Why is sample standard deviation a biased estimator of $\sigma$?, I am having difficulty understanding some of the steps. We have : (a) $s^2=\frac{1}{n-1}\sum_{i=1}^{\infty}(x_i-x\bar)^2$...
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### How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?

The formula for computing variance has $(n-1)$ in the denominator: $s^2 = \frac{\sum_{i=1}^N (x_i - \bar{x})^2}{n-1}$ I've always wondered why. However, reading and watching a few good videos about "...
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### Standard deviation of standard deviation

What is an estimator of standard deviation of standard deviation if normality of data can be assumed?
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### Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution?

It came as a bit of a shock to me the first time I did a normal distribution Monte Carlo simulation and discovered that the mean of $100$ standard deviations from $100$ samples, all having a sample ...
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### Calculating required sample size, precision of variance estimate?

Background I have a variable with an unknown distribution. I have 500 samples, but I would like demonstrate the precision with which I can calculate variance, e.g. to argue that a sample size of 500 ...
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### How can I find the standard deviation of the sample standard deviation from a normal distribution?

Forgive me if I've missed something rather obvious. I'm a physicist with what is essentially a (histogram) distribution centered about a mean value that approximates to a Normal distribution. The ...
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### How to calculate 2D standard deviation, with 0 mean, bounded by limits

My problem is as follows: I drop 40 balls at once from a certain point, a few meters over the floor. The balls roll, and comes to a rest. Using computer vision, I calculate the center of mass in the X-...
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### Is variance a more fundamental concept than standard deviation?

On this psychometrics website I read that [A]t a deep level variance is a more fundamental concept than the standard deviation. The site doesn't really explain further why variance is meant to ...