# Tagged Questions

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.

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### Motivation behind standard deviation?

Let's take the numbers 0-10. Their mean is 5, and the individual deviations from 5 are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 And so the average (magnitude of) ...
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### Sample Standard Deviation vs. Population Standard Deviation

I have an HP 50g graphing calculator and I am using it to calculate the standard deviation of some data. In the statistics calculation there is a type which can have two values: Sample Population I ...
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### Why is there not a simpler way to calculate the standard deviation?

Steps of getting standard deviation. http://www.techbookreport.com/tutorials/stddev-30-secs.html: Work out the average (mean value) of your set of numbers Work out the difference between each ...
Does anyone have an intuitive explanation (no formulas, just words! :D) about the "$n-1$" instead of "$n$" in the unbiased variance estimator $$S_n^2 = \dfrac{\sum\limits_{i = 1}^n \left(X_i-\bar{X}\... 4answers 3k views ### How can I calculate “most popular” more accurately? I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ... 2answers 5k views ### Recursive formula for variance I'd like to know how I can recursively (edit: iteratively) compute variance, so that I may calculate the standard deviation of a very large dataset in javascript. The input is a sorted array of ... 9answers 173 views ### Why is variance squared? The mean absolute deviation is:$$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$The variance is:$$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$So the mean deviation and the variance are ... 1answer 250 views ### Correctness of a statistical evaluation of a parameter I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ... 4answers 8k views ### incremental computation of standard deviation How can I compute the standard deviation in an incremental way (using the new value and the last computed mean and/or std deviation) ? for the non incremental way, I just do something like: ... 2answers 56k views ### Determining variance from sum of two random correlated variables I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated? 1answer 292 views ### Continuously sampled event: Estimating the value of a future data point, based on past measurements and their tendency Problem I'd appreciate some ideas on how to define a formula to estimate the value of a future data point for a continuously sampled event, based on past measurements and their tendency. At any ... 1answer 75 views ### Bootstrap method failing where blocking works I'm computing an average of individual samples that are not entirely independent and need an estimate for the true standard deviation. According to Newman and Barkema's book the most reliable method ... 1answer 1k views ### Denominator to calculate standard deviation I've just read something about calculating sample standard deviation. Some explanations say that it is because of degree of freedom. With a constraint that the mean should be zero, we do actually have ... 1answer 118 views ### Relation of mean of standard deviations and standard deviation Let \{x_{i,j} : i=1..7,j=1,..n\} be a set of samples from n weeks (where i denotes the day of the week). Is there any interesting information to be gleaned from the relationship (ratio, ... 1answer 68 views ### When plotting a bell curve from an array of values, is it possible that +/- 2 standard deviations from the mean can fall outside the range of values? First, this is not homework, it is actually for work. It's been a couple of years since I've done stats and need some help! I've googled for this problem but was unavailable to find any resources that ... 1answer 362 views ### Remove statistical outliers I've analysed newspapers by counting the language distributions of the articles. The results look like that: ... 1answer 938 views ### Uniform distribution, Expected value and standard deviation for proportion of observations in a subintervall X\sim U(0,1). Divide the interval [0,1] into k equal subintervals. Then X_1=the number of observtions on the first interval. Define the new variable Y_1=X_1/n, where n is the number of ... 1answer 41 views ### Method for determining the average deviation of data values over time? I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet. For convenience, I've set the minimum and maximum values on the y-axis to the weights that ... 1answer 141 views ### standard deviation find the probability that more than 30% A manufacturer produces a certain type of components that has a length of 2.1 \,\mathrm{cm}. the distribution of this components is normal with mean 2.15 \,\mathrm{cm} and sd 0.4 \,\mathrm{cm}. ... 1answer 303 views ### Measure dispersion of a set of values resides in a range I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ... 0answers 149 views ### Standard deviation of the mean through bootstrap resampling of dependent samples I'm trying to do a Monte Carlo approximation of an integral where the samples are not independent (how much so can be tuned by a parameter giving how often I sample). Therefore the regular expression ... 1answer 24 views ### Prove how to maximize Standard Deviation given a certain mean \bar{x} and set of values I'm talking specifically of population SD, where$$s = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2} I have a hunch that $s$ is maximized for a certain mean $\bar{x}$ when the values in ...
Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...