Linked Questions

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 ...

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 ...

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 ...

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 ...

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) $s^2=\frac{1}{n-1}\sum_{i=1}^{\infty}(x_i-x\bar)^2$...

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 "...

What is an estimator of standard deviation of standard deviation if normality of data can be assumed?

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 ...

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 ...

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 ...

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-...

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 ...

For the normal distribution, there is an unbiased estimator of the standard deviation given by: $$\hat{\sigma}_\text{unbiased} = \frac{\Gamma(\frac{n-1}{2})}{\Gamma(\frac{n}{2})} \sqrt{\frac{1}{2}\...

The skewness and kurtosis are defined as: $$\zeta_3 = \frac{E[(X-\mu)^3]}{E[(X-\mu)^2]^{3/2}} = \frac{\mu_3}{\sigma^3}$$ $$\zeta_4 = \frac{E[(X-\mu)^4]}{E[(X-\mu)^2]^2} = \frac{\mu_4}{\sigma^4}$$ The ...

would someone please explain why the degrees of freedom for a random sample is n-1 instead of n ? I'm looking for an explanation that is intuitive and easily understood by a high school student.