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Questions tagged [standard-deviation]

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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How to quantify the fluctuation of an error?

First of all sorry for the bad title, but unfortunately, I can't think of a better one at the moment. Hopefully, that will change when my question is answered. Let's say I have two sets of values: ...
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How to calculate the standard deviation and mean of a group of individual statistics

Is there a formula to calculate the standard deviation of a group or individual statistics Example in a sporting fantasy league I can calculate the summary statistics of any one player. Example ...
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If I take mean of uncertain observations what happens to SD of the observations?

I have some observations, each with an accompanying standard deviation (shown here as error bars): I want to make a summarised plot of this data by taking mean of all observations for a given X value,...
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Why is the population standard deviation approximated as the sample standard deviation?

This question addresses calculating a p value from the mean and standard deviation statistics of a sample. I understand that the -general- philosophy is to divide the sample standard deviation by the ...
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Propagating error when taking the derivative

I have a function that corresponds to a set of $(X,Y)$ coordinates with a Gaussian uncertainty ($\sigma_Y$) for each point. What I want to do is now compute the gradient of this function and the ...
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2answers
46 views

Developing a 40-100 scoring system (doesn't work as intended) [on hold]

I am using r. I have a dataset with this distribution There are 1275 observations with values ranging from ~ -0.07 to mostly 0.08. I have 4 outliers that are over 0.8 (0.12, 0.12, 0.12 and 0.10). I ...
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How to read the mean and standard deviation from a Q-Q plot

I wrote the following code in R to make the following qqplot. In a question I am asked to read the mean and standard deviation of the sample off the plot. I see ...
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How does the nth sample impact Mean and Variance? [duplicate]

Given the Mean and Variance of $n$ samples $x_i$: $$M_n=\frac {1}{n}\sum_{1}^{n} x_i$$ $$V_n=\frac {1}{n}\sum_{1}^{n}(x_i-μ_n)^2$$ How do Mean and Variance change, when we take into account one ...
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Is it possible to calculate standard deviation from d (effect size)? How do you do it?

I am doing a meta-analysis and one of the papers report d instead of SD. I do also have sample size and mean for each group, but I don't have the SD for each group.
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Calculating change in mean and standard deviation of Sample X due to replacing p% of X with data from another distribution

Suppose we have two independent normal distributions $A \sim \mathcal{N}(\mu_a, {\sigma_a}^2)$ and $B \sim \mathcal{N}(\mu_b, {\sigma_b}^2)$. Suppose that we have a sample $X$, which is drawn from $A$...
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Proper way of calculating statistics for samples probabilites [closed]

I have 64 samples and for each one of them, I have their probability. I was wondering which is the correct way to find a mean and std for the above-mentioned population. If I do something like: <...
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How to identify if standard error is stable?

I am doing some genetic simulations and I want to stop them when the standard error is "stable", i.e. the variation is not too high. The goal is to avoid wasting time and computational resources. I ...
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What will be the confidence interval(for below question) for 99 percent confidence level [68 95 99 rule] [closed]

Is the below solution correct....because the probability of obtaining a sample which would have the mean height of 70 will fall under the intervals calculated using the mean+/- 3(SD) [99% Confidence ...
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31 views

Find confidence interval of mean without knowing sample size?

In our calculation, we have only $\mu$ and $\sigma$ values. Is that possible to find the confidence interval of $\mu$ and $\sigma$, without knowing the sample size? As per our idea, we can calculated ...
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MLE standard errors: complex from optimizing negative loglikelihood using fminunc

Does anyone know what goes wrong when fminunc in matlab returns a hessian of which the square root of the diagonal of the inverse hessian provides complex numbers? The complex numbers arise due to ...
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different results grouped survey standard deviation in Stata and R

I have a question concerning the calculation of the grouped variance or standard deviation in R (survey-packge by Thomas Lumley) and Stata (using svyset and svy prefix). I'd like to know if there ara ...
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Degrees of freedom for two-sample t-test of predicted means (MLR)

I wonder how to decide if two regression models are significantly different at a location X. Here is an artificial example, $\hat{Y}=a+b\cdot X+c\cdot X^2$. The graph shows the (artificial) measured ...
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Calculating Sample Size As Number of Days Needed For Significance?

I am trying to determine required number of days required to reach a significant result for a one-tailed independent sample test. I have sales data by day for my test and control group. The results ...
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Is the Coefficient of Variation valid for data which does not follow a normal distribution?

I am trying to compare the dispersion of several data vectors. As an example I have that via two methods produces one vector of data that fits a normal distribution and other one that follows an ...
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Correct order for computing standard error of the mean of means

Good afternoon, I read some related questions but there is still some things I can't quite wrap my head around. Let's say I want to average some time series over X subjects, Y channels, and, ...
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Calculate SD for a given problem specification (see Body) with python

I am new here as you can tell. I have the following problem for which the SD has to be adjusted in order to fit said problem. Problem: Say I have 500 balls which I deliver to a customer and if more ...
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Need clarification for different notations and corresponding formulas in Linear Regression

1) First of all, can anybody clarify, whether my notations correspond to the correct formula. As I found different descriptions/notations for different formulas, I tried to put these Information ...
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Confidence interval before or after target variable transformation?

I created a machine learning model where I normalized the target variable in the training set before fitting the model. I then used a package which produced a standard deviation of eqch prediction. If ...
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1answer
34 views

If sample standard deviation is biased, why do we use it in typical mean tests? [duplicate]

If sample standard deviation is biased, why do we use it in typical mean tests? Why do we not use an unbiased estimator by dividing the sample standard deviation by C4?
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Inconsitency in comparing log-likelihoods of z- and t-values with appropriate distributions?

I am working through "Glen McPherson: Applying and interpreting statistics", where he introduces the t-distribution on p.125. As a small experiment i tried to do the following (pyhton, scipy, numpy, ...
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Association of binned data

this is my first question here, hoping you all can help. I have tenure and age data for an organization that has been binned already, and unfortunately don't have access to the actual ages/tenures of ...
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Compare variables with zeta-score

Assume the calculation of a physical quantity $x$ from a given formula i.e. $$x=\dfrac{a*b}{c}$$ where $a, b$ and $c$ are experimental observables, therefore $x$ is a quantity derived from ...
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1answer
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Estimating sample size needed to reach estimate precision (Bayesian CIs)

I want to estimate the required sample size to reach a specified width (precision) of the Bayesian credible intervals of the parameter of interest by using the standard error (posterior standard ...
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Average of several standard deviations

My aim is to calculate the measurement precision of a measuring device. To do so, I measure a part three times and calculate the standard deviation. Unfortunately, it is not possible to measure the ...
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1answer
53 views

Regression and Standard Deviation

When I plot my Regression Line and the corresponding lines for 2 standard deviations, sometimes it happens, that no values lie outside the 2 standard deviations. Is that possible/correct or must there ...
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4answers
1k views

Assuming a normal distribution: what is the sd for a given mean?

Assume that accordning to a national statistic people in germany have a $mean$ of $10,000$ € on their bank account and we call that their "assets". Unfortunattely, only the $mean$ is given but not the ...
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37 views

Which formula for t-test is correct?

When Population variance is unknown and n<30 we use t-test. x=sample mean, u=population mean, s=sample standard deviation, In my book and on many online websites i found t-test formula to be t=(...
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How to calculate the percentage of values that lie within some range of Standard Deviation around the Mean in a Normal Distribution Curve) [duplicate]

This wiki article on 68–95–99.7 rule states - In a Bell Curve (i.e Normal Distribution Curve), 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, ...
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How is standard deviation impacted by adding an array of values to itself?

Consider the following example (python 3 code): ...
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Is it possible to calculate the standard deviation of a set that is built from moving averages?

Hope you are all doing fine. I need to calculate the probability of the performance of a X player increasing or decreasing in time. For each ball the X player kicks, he can either score (1) or miss (...
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Newbie wondering about standard deviation and how to detect outliers in new datapoints

So I have a dataset, with the count of records processed per day in each, e.g. | 27th April: 3491 | 28th April: 2058 | 29th April: 9321 | 30th April: 1021 I want to be able to take a new day's count ...
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central limit theorem: do we care about standard deviation within one sample of size n? [duplicate]

I'm learning applications on Central Limit Theorem and got really confused with a few points. Think of an example of applying Central Limit Theorem: We have a whole population of 10 billion items ...
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Do we use the SD of whole population or SD of just one sample to calculate SE of samples means in central limit theorem?

I'm learning applications on Central Limit Theorem and got really confused with a few points. According to this tutorial, the procedure to apply CLT usually goes like this: So if ...
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How to standardize data with low variance?

I have quarterly data of federal fund rate (test set), e.g.: ...
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Unbiased Estimator of the Standard Deviation of the Sample Standard Deviation

I'm looking for an unbiased estimator of the standard deviation $\text{SD}(s)$ of the sample standard deviation $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}$. I have found this ...
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Coefficient of variation and residual standard deviation

From my knowledge, coefficient of variation and residual standard deviation are highly correlated. Such that if we find a significant change in one, we will find a significant change in the other. In ...
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1answer
115 views

Compute standard deviation of accuracy

edit - more information about what the code given should represent The following pseudocode outlines the problem as I have it ...
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Qualtrics and Epi Info yield different Standard Deviation values?

Uncertain if this is the correct place to post this, but I'll give it a shot. I'm a Master's Student working with a small (n=25 respondents) data set. I originally entered my surveys into Qualtrics. ...
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32 views

Name for Standard Deviation over possible range (1-255)?

I have RGB brightness values over a possible range of 1-255. I am already computing Coefficient of Variation, but since my domain is strictly limited, I am interested in seeing a measure of how spread ...
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28 views

Mean Absolute Deviation and sum of independent random variables

Consider the sum of 2 independent random variables $P$ and $Q$ with unknown distributions. It is known that the variance of the sum of the variables is the sum of the variances. Is there any ...
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1answer
24 views

what is the difference between Standard error of the means vs Sampling error?

I am confused after learning about the different terms. I understood Standard error of the means to be the Standard Deviation of the sample means, whilst Sampling error is the Standard Deviation ...
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How to evaluate the degree to which survey results are scattered

Let's say I have a number of numeric answers from a group of people and I need to decide whether the group agrees on the question or not. I can imagine doing this by calculating standard deviation of ...
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1answer
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Geometric mean and geometric standard deviation

When summarizing normalized data (for example, percentage data), one must use the geometric mean instead of the arithmetic mean. Thus, instead of using the arithmetic standard deviation, one shall use ...
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Calculate Percent Change after running Paired Samples T-test

I have two measurements pre and post. I ran a paired samples t-test to determine if a statistically significant difference exists between pre and post. I would like to report the Percent difference ...
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overall variance of different time signals

I have two sensors mounted on two appliances and they measure a variable in the time domain every 1 second. Now for the course of 1 hour, I want to make only one error bar that contains both signals....