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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Sample size calculation for AB testing in offline scenario

I have sales data for 500 stores and lets say I want to run an AB test on a sample of test and control stores with the objective of getting statistically significant increase in sales(lift). My ...
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Use standard deviation of sample or population in z test

I am reading the book Statistics by Witte & Witte. Some questions puzzle me. Question 10.9: The normal range for a widely accepted measure of body size, the body mass index (BMI), ranges ...
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How can I calculate the effect of linear interpolation on the standard deviation?

So I have amplitudes following a normal distribution with $\mu = 0$ and $\sigma = 1$. Now a certain amplitude "live" for a fixed time and then a new one is drawn from the distribution. Due to physical ...
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How to derive this inverse standard deviation error bound for binomial random variable? [duplicate]

Is this error bound suggesting the normal approximation is good for binomial random variables? How was it derived? Why is the reciprocal standard deviation in the error bound?
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What can I say with mean, variance and standard deviation?

I wrote this code in R: ...
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Why are there two ways to calculate the standard deviation of a binary variable?

I've always been told that the standard deviation of a binary variable is sqrt(npq). However, there also appears to be a different way to calculate it: ...
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How can I compute standard deviation without k observations

For a given variable $X$, we compute the standard deviation. Now I removed $k$ observations from $X_n$ and I would like to compute the new standard deviation $\sigma_{(k)}$ using $\sigma_{n}$. I ...
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Relative Median Absolute Deviation

For example, the CV (coefficient of variation) is the relative standard deviation (sd divided by the mean). Now is there a relative MAD (Median absolute deviation https://en.wikipedia.org/wiki/...
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standard deviation formula --population or sample

if given a set of data say 10 numbers, which one should we use standard deviation or sample standard deviation.there is no mention of sample or population in the problem.
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Mean average error normalized by the standard deviation of the target

I'm working on a regression model, aiming at prediction age from structured data. I'm using the mean average error (MAE) as evaluation metric, and want to compare my performances with state-of-the-art ...
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how to detect a 5% deviation between more than 2 numbers

Dear StackExchange Team in the industry there are GAs generators that have hundreds of instrument measuring process values, such as pressure, temperatures, etc. we have a simple case where a ...
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Explaination behind the relation between the correlataion coefficient and distance of a typical point from the standard deviation line

I am reading a textbook on statists by Freedman, Pisani, and Purves. In one of the chapters about correlation between two variables, it is given that the vertical distance of a typical point from the ...
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How to calculate the threshold value for a variable

In a question-answer platform, in each week the platform releases a new question. In total there are 15 questions. There are these three types of users. Log in every week, and answer in the correct ...
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The difference between approaches to find 95% interval in normal distribution

I ran across two very similar problems but each one's supposed answer is approached very differently. Problem 1: A large study of serum folate levels in a sample of women age 16-45 reveals that ...
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Test for significant difference from zero

I have a set of actor's activity coefficients for different subjects for every day in a given time range, which looks like this: ...
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Stnadard deviation of values containing different ranges

Taking the $\sigma$ of these values : np.std([55,50,40,45]) returns: 5.59 If I take the $\sigma$ of these values: ...
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What are some techniques for communicating data distributions to unsophisticated users?

In my scenario, students are grouped into classes and each student has a performance metric. I want to be able to show teachers and principals a list of classes, along with an aggregate performance ...
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A variance measure for a variable that takes both positive and negative values with the mean close to zero

I've been using relative standard deviation as a measure of variance for my variables, but some of them take both positive and negative values and their mean is close to zero, so it's not a good ...
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Standard error of mean calculation — pooled samples vs. unpooled

I'm trying to understand why the standard error of the mean changes depending on how measurements are pooled into samples, even if the total measurements are the same. For example, the following two ...
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Is it possible to derive standard deviation from confidence interval?

is it possible to derive the standard deviation from data described with mean and 95% confidence interval? If I have a distribution with a mean of 2.5 (1.5-4.0), ...
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Standard Deviation - Practice Exam Question Error?

I'm taking an online practice exam to prepare for a real test. This question appeared and I believe I'm answering it correctly but the online practice exam scoring engine keeps telling me I'm wrong, ...
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The Distribution of sample standard deviation from a chi squared parent

Suppose we have k groups of n i.i.d observations which follow the Chi-squared parent distribution with 1 degree of freedom. The sample standard deviation S is a random variable (with k available ...
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Standard Deviation of a Ratio of Two Numbers with Different Standard Deviations but High Correlation?

I have two means that are highly correlated (R = 0.83) with normal distributions but with different standard deviations. When I divide the two means to get a ratio, how do I calculate the standard ...
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Calculate standard deviation of a set of numbers in one cycle over the numbers without knowing average in advance [duplicate]

I have an set of numbers that I need to calculate standard deviation of. I want to do it in a single cycle over that set and I don't know the average of the array beforehand. I need it for my program: ...
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Population Variance from Random Samples of Normal Distributions

Let $(x_1,x_2,\ldots,x_7)$ and $(y_1,y_2,\ldots,y_{49})$ be two simple random samples from two independent populations whose distributions are $N(\mu_x,\sigma)$ and $N(\mu_y,\sigma)$, respectively. It ...
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Questions about Confidence Interval

could somebody please help me with this question. "What will happen to Confidence Interval if you change from using sample SD to population SD? Would the CI you calculated previously increase, ...
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Not sure about T test's sample size

I have a dataset that has when a user clicked over a period of 31 days in an app. Its possible that all users won't have 31 days of clicks as they might not be using the app on a particular day. The ...
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The standard error for two sample means that are come from other population

Hi I'm now finding the standard error for two samples that are come from other population when the sample means are not independent. I have written the result when the sample means are independent. In ...
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Opinions on a statistical error in p values (re: standard deviations, t-test/Kruskal-Wallis) in a published study?

Following a question I asked recently and the discussion which ensued, I'd like to pose a specific question to the community. The study in question is Ozbay et al., it pertains to tinnitus (phantom ...
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How to compute robust normalized relative variance of a small set of numbers

I am looking for a way to calculate a statistic that represents the normalized robust relative variance or spread of any relatively small set of numbers. Concretely, I would like to compute a ...
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Write pseudo-code describing an algorithm to compute the p−value for an observed statistics tobs

Using R code I have to write a pseudo code and real code to answer this question. I am currently at a point where I have the following: test statistic= sqrt n (Y bar - mu) all over the standard ...
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Cramér-Rao lower bound with an uncertain observable

Let's say I have an observable $X$ that depends on a parameter $\theta$, and that I can find an expression for the Cramér-Rao lower bound for estimating $\theta$, as a function of $X$: $\sigma_{CRB}(X)...
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How to compare the results of Monte Carlo simulations with different sample sizes?

I'm simulating the Monopoly game and trying to find out the most frequent squares in the board. For further details, it is Project Euler problem 84. The solution will not be spoiled. To illustrate ...
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How to deal with two sources of sampling error on same sample… add? multiply?

I'm working with a sample of samples, by which I mean each item has an individual standard deviation, and I have a random sample of the total items. To get the standard error of the mean of my sample,...
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Sampe Standard deviation, what distribution does it follow?

Suppose we have $k$ groups of $n$ i.i.d observations which follow the $N(0,1)$ parent distribution. The sample standard deviation $S$ is a random variable (with $k$ available observations), do we know ...
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How to calculate the mean and SD of a new parameter using two groups mean and SD

Hello I have a problem to calculate the mean and SD of a new parameter using two groups mean and SD. I have the means X1 and X2 and the SD as S1 and S2 I want to create new parameter Y = X1/X2 What ...
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How can I determine if most of my values are above or below average?

How can I tell if the majority of my data is either above or below my average? 8 8 7 5 4 9 8 9 9 11 13 AVG = 8.272727273 MEDIAN = 8 PERCENTILE 0.5 = 8 If my ...
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Normalized statistical measure for agreement of biological replicates

I've conducted an experiment collecting samples from various depths in the ocean. At each depth, I collected 3 samples to act as biological replicates. I now want to show that all of my replicates ...
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Unbiased estimator of standard deviation

I'm reading "Properties of range-based volatility estimators" where the authors talk about using the range of a distribution ($h$ - $l$) to estimate its volatility. Specifically, they say, Daily ...
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What is the proper formula to highlight variance in utilization

I have $160$ machines that are given tasks over time. Each machine is expected to perform $\frac{1}{160}$ of the overall tasks, however if one encounters a fault, it could have some period of ...
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The data set missing values and percentage of data that would remain unaffected

Can not understand question and answer to it given on DS questions site (see link below): Q3. You are given a data set. The data set has missing values which spread along 1 standard deviation from ...
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Confidence intervals confusion

I'm looking at a problem where the number of samples, $N$, is 2 million. Each sample represents a profit or loss. Let $X_n$ be the dollar payoff to the n-th game. $E[X_n] = 0$. Let the total payoff of ...
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Estimating population standard deviation from subsample means [duplicate]

I would like to estimate the standard deviation of a population. The data I have is the size and mean of each of $k$ independent uniform subsamples: $(n_1, \mu_1), (n_2, \mu_2), \ldots, (n_k, \mu_k)$. ...
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Shortcut for calculating the standard deviation of a binomial outcome?

We can see the equations for how to calculate the sample standard deviation, and perform these to the sample. If our sample only ever consists of 0s and ...
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Why does the standard deviation sum squares of deviations from the mean instead of absolute deviations? [duplicate]

(This is a question from a friend of mine who is a secondary school mathematics teacher --- I am posting it on his behalf.) My question is about the standard deviation. I was talking to a colleague ...
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Division of two values that are represented as MEAN+/-STDEV

Look at the article here (https://pubmed.ncbi.nlm.nih.gov/1618464/) (I am not sure if you have access to the full article, if not, let me know so that I can find a way to share it). Basically, they ...
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Will change in standard deviation impact covariance?

If we increase the degree of standard deviation of one variable, does it affect covariance of two variables? Example, two variables are there, A & B, the covariance of A & B is 100, and the ...
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Standard error questions

This is an elementary question, but I'm a bit confused on the concept of standard error. On some sources, I've seen that standard error is defined as the standard deviation or the square root of the ...
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Why in some cases it makes sense to multiply Stdev by the Sqrt(N)?

I found an example when a so-called volatility index is calculated by multiplication of a sample standard deviation by the ...
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How do you calculate standard deviation for a mean change, given mean 1, SD 1, mean 2, SD 2, and total n?

How do you calculate standard deviation for a mean change, given mean 1, SD 1, mean 2, SD 2, and total n? For example: n=590. Initial mean is 26 with a standard deviation of 8. The mean at the end ...

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