Standard deviation is the square root of the variance of a random variable, an estimator thereof, or a similar measure of the spread of a batch of data.

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The standard normal distribution vs the t-distribution

Given an IID normally distributed sample $X_1,...,X_n$ for $n$ small with mean $\mu$, standard deviation $\sigma$, sample mean $\overline{X}$ and sample standard deviation $s$ (the unbiased estimator ...
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5 views

Standard deviation of multiple root mean square values

I am calculating the R.M.S. of a periodic signal that has a stochastic component to it. For every period I am able to calculate a value for R.M.S. using the following function: $R.M.S. = ...
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2answers
96 views

What does standard deviation tell us in non-normal distribution

In a normal distribution, the 68-95-99.7 rule imparts standard deviation a lot of meaning. But what would standard deviation mean in a non-normal distribution (multimodal or skewed)? Would all data ...
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1answer
27 views

Standard deviation when sample is significant part of population

I know that sample standard deviation and population standard deviation are different, and are used in different cases (first when N>>n, second when N=n). But what when N>n, although not by much? For ...
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67 views

Confidence interval for poisson distributed data

I'd like to calculate the confidence interval for a variable with a lower bound and I can't seem to figure out how to do so. I've seen several similar posts, but none answered my question, at least ...
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17 views

How to calculate the standard deviation from a normalised value?

I have 2 data sets (I have more but for simplicity lets say I have 2). Data 1 0.15239652 0.145848036 0.175981261 Data 2 0.417902092 0.342696648 0.354871141 I ...
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9 views

Combining Standard deviation 3 groups

Is this the correct formula for combining the standard deviations of 3 groups? $$ \sigma = \sqrt{\frac{n_1\sigma_1^2 + n_2 \sigma_2^2+ n_3 \sigma_3^2+ n_1(\mu_1-\mu)^2 ...
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1 views

Structural changes in the observed standard deviation

Supposing to have a stochastic process with known normal distribution N(m,s) we can observe samples from. For quality test purpose, we define a threshold for good/bad samples equal to 3 standard ...
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1answer
123 views

How to calculate SD of sample for one new observation?

In below example, Is it possible to calculate new SD for one additional observation? In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following ...
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15 views

A method to find the inconsistency or variation in the data

I am running an experiment (it's an image processing experiment) in which I have a set of paper samples, and each sample has a set of lines. For each line in the paper sample, its strength is ...
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39 views

Questions about G*Power

Since I found an insignificant result, I performed a power calculation in G*Power. But I am not entirely sure if I input the right number in some fields. My design is a 2(between Ss) x 2(between Ss) ...
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1answer
22 views

On the connection between SSE and absolute deviation from the centroids

Is there any connection between sum of squared error SSE and the absolute deviation from the centroids after clustering. More formally, I have clustered $T=\{x_i\}, i\in\{1,\ldots,n\}$ and the ...
3
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1answer
144 views

Question about standard deviation and central limit theorem

I have a quick question about the central limit theorem. Lets say I measure some value that comes from an arbitrary distribution N times and I repeat this M times. I understand that if I calculcate ...
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21 views

Relative importance of variables?

The following output is given: The task is to state, which variables, among thoses that are statistically significnat at 0.05, have the greatest and least relative importance on the fitted model? ...
3
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1answer
47 views

Determining Whether Values Within One Standard Deviation Meet Some Condition

Suppose I have a set of objects, each of which can take on values within some unknown range, and each of which only has one sample of 50+ values associated with it. The values of each observation is ...
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28 views

Adding mean and standard deviation to each other

I make a certain measurement and I would like to arrive at a single descriptive number that would give me an idea of both the average value of the measurement, as well as the deviation from the mean. ...
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1answer
26 views

How to measure dispersion of a single point within a group of points

Lets say you are given a set of $n$ points and for each one, you want to get a measure of dispersion of its closest $d$ points. So a point far away from others will have a large measure of dispersion ...
2
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1answer
59 views

Calculating sample size with unknown standard deviation

I'm having troubles with understanding a problem which is basically asking to calculate a sample size (in order to estimate what portion of population has income more than 40K) with ...
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19 views

Regression with standard deviation dependent on predictor?

I got this question of how to deal with a regression model involving a set av predictors. The model wanted was one where the response should be divided by the (non-constant) standard deviation of the ...
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1answer
28 views

What is the likelihood of an observed standard deviation given a known normal distribution?

Given a sample X of size n from a normal distribution $N(\mu,\sigma)$ one can estimate $\sigma$ by $\hat{\sigma}$ from X. Then we know that: ...
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98 views

Standard deviation for a measurement that has two causes of uncertainty

I would like to know how to calculate the standard deviation for a measurement value $x$ when there are two separate sources of uncertainty, 1 and 2, each with known standard deviation, $\sigma_1$ and ...
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1answer
22 views

Use of standard error of the mean when the components are not identically-distributed

Let {$X_1$, ..., $X_n$} be a random sample of size n in which the different elements are measurements drawn from $m$ different populations with different distributions. From the Central Limit Theorem, ...
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2answers
126 views

How do you calculate the standard deviation for Roulette?

I've seen quoted in a number of places that the standard deviation for a 1-number bet on a 38 number Roulette wheel (0, 00, 1, 2, .., 36) is 5.76. I can't seem to find a single source that shows how ...
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31 views

Standard deviation in Weibull distribution

I've have a script that creates Weibull distributions with a static shape parameter and a variable scale parameter, the scale parameter changing to yield a distribution that meets a specified mean ...
0
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1answer
40 views

Calculation of sigma with Gaussian distribution

I am looking for a Gaussian function centered in $0$ with $90\%$ of the integral is in $[-10,10]$. From this information, how can I get the value of $\sigma$? I guess we can write $P(|X|<10)=0.9$ ...
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33 views

MCMC Standard error

I need to make a simulation to calculate the integral of a pdf $f(x|D)$ over a region $T$.That is, I need to evaluate $$\int_T f(x|D)\; dx$$ to do this, I just defined the function $g(x)=1$ if $x \in ...
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26 views

MC Standard Error for Metropolis Random-Walk Algorithm

I need to calculate some integrals using MCMC with Metropolis Random-Walk Algorithm. To decide the value I will accept as my integral, I will calculate 5 simulations of MCMC with size 2000, but I ...
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1answer
57 views

Standard deviation exceeds maximum value

I am trying to plot data that only has two possible values – 1 (present) or 0 (absent) – clearly not a normal distribution. The ...
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1answer
88 views

Calculating the variance of the histogram of a grayscale image

I am doing image processing and I want to calculate the variance of a histogram of pixel intensities. The first method I have tried: The images store the pixels values using double precision ...
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43 views

Calculating NBA shooting consistency

What would be the proper way to evaluate/determine an NBA player's 3-point shooting consistency? For instance, I have a player that shoots 37% from 3-point range and takes 200 attempts all year. I ...
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1answer
49 views

Given the distribution of a variable X, what is the distribution of f(X)?

Suppose I know the mean and standard deviation of a (roughly) normally distributed variable x. Is there any way for me to calculate the mean and standard deviation of f(x)? The particular problem I ...
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0answers
37 views

How to calculate 'weighted' pooled/composite statistics for two given groups given group statistics

I have two sets of independent samples from the same distribution. For each, I have calculated sample weighted mean (u1, u2) sample weighted std deviation (d1, d2) sample weighted std error (e1, e2) ...
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67 views

Practical meaning of expected value, standard deviation & correlation

We've got given annual results of two stock companies described with following values: Company X: expected value $\mu_X=0.05$, standard deviation $\sigma_X=0.02$ Company Y: expected value ...
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35 views

Is it reasonable to measure standard deviation from true value rather than mean?

I am evaluating the accuracy of GPS watches, taking many readings over a known distance. I've been calculating standard deviation using the mean reading, but because I know what the reading should be, ...
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How to calculate a maximum standard deviation? [duplicate]

I have a test which contains 24 items, so the maximum result is 24 and the minimum result is 0. How can I calculate the maximum standard deviation possible? Thank you!
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How to create a weekly alert system that works for different sample sizes?

I'm trying to build a weekly alert system to let me know when something unusual has happened in my analytics data that might require further investigation. Currently there is an outdated system in ...
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44 views

What if sample size is larger than population size?

I read something about standard error, which tells that sample mean is not accurate estimation because we do not sample full population of size N. But, what if sample size n = N or exceeds N, i.e. n > ...
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26 views

standard deviation set for spline cubic regression model

I'm attaching two sets I ran in SAS, regarding spline cubic regression models. I'm new to stats and trying my best to learn but I'm stuck here. How do I get SAS to select outliers based on two or 3 ...
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1answer
24 views

Question on Portfolio Risk & Covariance

Good evening, I was reading a stats textbook where I came across the following statement: In order to reduce the portfolio risk of a portfolio involving two risky investments, we should choose ...
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1answer
97 views

Least Squares Fits to Experimental Data

My attempt at making sense of the problem: The problem provides us with the sum of squares (SS; I believe that's the $18.1$). We can use the SS along with the number of samples $(21)$ to get the ...
6
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1answer
140 views

Required number of simulations for Monte Carlo analysis

My question is about the required number of simulations for Monte Carlo analysis method. As far as I see the required number of simulations for any allowed percentage error $E$ (e.g., 5) is $$ n = ...
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Identifying patterns in data streams with minimal state

I could not pick a more generic title for this question I guess. Here is what I am dealing with: I have a time series data stream coming in from multiple measurement endpoints. The number of ...
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1answer
121 views

Why is variability measured relative to a point?

Why are measures of dispersion calculated relative to some central point? Why wouldn't, for instance, all possible non-repeated, pairwise differences in the dataset be a valid measure of spread?
2
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1answer
30 views

What quantifies a stable parameter?

I'm optimizing 5 parameters for an option pricing model. Now I want to asses whether these parameters are stable over time (i.e., a year). For this I create about 12 subsamples and estimate the ...
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1answer
35 views

Standard deviation of a sample when you know the average

I'm coding an app, a part of which is graphing values from a database. The graph plots the average value of every 10% of the values up to 100% so there are ten points along the x-axis. The graph ...
2
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1answer
23 views

Measure of intermittency/continuousness of a signal

I have three signals (below) each having the same standard deviation, however, are clearly very different temporally. Is there some such metric that could be calculated for each of these signals to ...
0
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1answer
60 views

Combining results of two samples to find combined standard deviation

I was making an attempt to solve the following problem sets, however, my answer 15.913 seemed quite different from that in the answer key 16.84. I have checked my answer a few times and re-doing the ...
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39 views

Calculation of standard variance $s^2$

First picture is the question and its answer key: The second picture is my solution: I know that $S^2=\frac{\sum(x_i-\bar x)^2}{n-1}$ But in the answer key, $s^2$ cannot be found in that way. ...
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1answer
114 views

Calculating scale mean from item means

I'm working on a review paper and need to collect the means and standard deviations of a given measure (such as a measure of depression) from papers of interest. However, some authors report means and ...
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129 views

Standard deviation of normalized data

I have a data set $y_i$ (where the $y_i$ are photon counts in time period $i$, $i=1,2,...,n$, assumed Poisson), with an estimated standard error $s_i$ (= $\sqrt{y_i}$) for each count. For some ...