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 derive quantiles of a non-standard normal distribution [duplicate]

Let X = [11.17, 9.52, 10.69, 9.84, 10.84, 9.88, 10.28, 12.23, 8.49, 10.79] be a normally distributed data with mean = 10.37 and standard deviation = 1.02. How to determine the corresponding value to ...
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estimating the population standard deviation from the sample standard deviation

Is there a way to estimating the population standard deviation, $\sigma$, from the sample standard deviation, $s$, if the size of the finite population is $N$ and the size of the sample is $n$? Is ...
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41 views

How to name the concept of the mean shift divided by the standard deviation

In the context of a paper dealing with Statistical Quality Control, I am defining and using the concept of the mean shift divided by the standard deviation of a (normally distributed one-dimensional) ...
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11 views

Choosing between two parameters based on the mean and the standard deviation of the error

I am trying to interpolate data under the assumption that I have the true data. The interpolated data is dependent on a parameter which I am trying to estimate. For each possible value of this ...
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10 views

Role of Chi inverse distribution in the confidence interval of standard deviation

Suppose X = [11.17, 9.52, 10.69, 9.84, 10.84, 9.88, 10.28, 12.23, 18.4] is a random variable with mean and standard deviation as 11.48 and 2.77, respectively. If I calculate the lower and upper ...
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What is the confidence interval for model that is supposed to have mean of 'zero'?

I'm trying to analyze some dataset. I have a model. This model predicts some values. There are real values also known. I calculated the differences between the predicted and real outputs. Ideally, the ...
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1answer
182 views

Area within a given number of standard deviations from given mean

I have a variable with mean value of 18.85 and standard deviation of 1.45. I want to define the area that is covered by 1.45 standard deviations left and 1.45 standard deviations on the right side ...
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10 views

Optimal length of observation window

I have a sample of N stocks, with time-series of daily returns. For each stock, I would like to compute the sample univariate variance of returns, using a rolling window. These variance will be used ...
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10 views

Normalisation formula applicable to one or more data items

I've created a recurrent neural network, to which normalised values are passed as inputs. The normalization formula is: $$\tilde{x_{i}} = \frac{1}{1+exp(-\frac{x_i-\bar{x}}{\sigma})},$$ where ...
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1answer
57 views

What is the probability that a girl is taller than a boy, with boys ~N(68, 4.5) and girls ~N(62, 3.2)?

"Given that boys' heights are distributed normally $\mathcal{N}(68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal{N}(62$ inches, $3.2$ inches$)$, what is the probability that a girl ...
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41 views

Intuition for what happens to the standard deviation after plugging a normal variable into a function

Let's say I have a normal variable $X$. I feed $X$ into some function, which applies varies mathematical operations to it - for instance, addition, subtraction, multiplication, division, $x^r$, $e^x$, ...
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525 views

Can mean plus one standard deviation exceed maximum value?

I have mean 74.10 and standard deviation 33.44 for a sample that has minimum 0 and maximum 94.33. My professor asks me how can mean plus one standard deviation exceed the maximum. I showed her ...
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7 views

Weighted Standard Deviation [duplicate]

I got a problem calculating a weighted standard deviation for a municipality and its precipitation on various landcover types (LC). I got the mean values of precipitation for several days for each ...
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24 views

z-score and Normal Distribution

I have what is probably a pretty stupid question but for whatever reason I have not been able to find an answer so here goes.... It's my understanding that a z-score can only be calculated and ...
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13 views

Standard deviaiton for mean of an already averaged data

I was wondering how to set the standard deviations for average of an already averaged data! The following example shows 2 countries, each with 3 districts. From each district samples (n) were ...
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27 views

does multiple regression sound right?

we provided a hot/cold description to students of a Male/Female substitute professor and asked them to rate them on a likert scale (1-7). With this data, I would like to see if there is a relationship ...
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22 views

How to find normal quantiles?

A social psychologist interested in eating behavior wanted to divide students into four groups based on their eating proclivities. The four groups were those who were restrained eaters, moderately ...
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31 views

Using STDEV and RANGE to subset data to desirable subjects

I am running several subjects through a mixed model regression and have encountered problems in which several of the subjects have an undesirable distribution for the specific study I am performing. ...
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55 views

Why is the standard deviation of the sample mean less than the population SD?

The sample means do not vary as much as the individual values in the population. That the sample means are less variable than the individual values in the population follows directly from the fact ...
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10 views

Is this estimator for the standard error of a sample mean difference biased and what is the relation to Student's t-test?

In the situation of two indepdent samples, the variance of the difference in sample means $\bar{x}_1$ and $\bar{x}_2$ is $$Var(\bar{x}_d)=\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}=\sigma_d^2$$ and ...
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1answer
25 views

How to compute the standard deviation of residuals from a regression line or curve?

After fitting a line or curve, it is easy to compute each residual as the difference between the actual Y value and the Y value predicted by the model fit by regression. For standard regression, the ...
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80 views

Confirmation of normality using residuals from an linear regression

95% of my residuals from an linear regression lie within 2 standard deviations of the predicted values. Is this enough to confirm normality or could any other distributions have 95% of residuals that ...
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182 views

Why doesn't the standard deviation represent a normal distribution?

Why doesn't the standard deviation of a sufficiently large sample represent a normal distribution that we can make inferences from? Let me list my thought process, so hopefully someone can highlight ...
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51 views

Better than Mad, Derive $Q_n$

Could someone be so kind as to walk me through how to do this equation on a dataset? on pg 5 (marked as 1277) equation 3.3 of this paper. $$Q_n = c|x_i-x_j|_{(k)},\;\;1\leq i<j\leq ...
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21 views

Multiple Comparison of Standard Deviations

I have a question about comparing multiple standard deviations: To start with, let's say I have calculated two standard deviations (s1, s2) from a series of random samples. If I want to determine ...
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12 views

Combining two estimates of variance

I have a sample of N stocks, and a sample period of length T. At each time $t$, I have the following information: For each stock i, I have an estimate of variance (of returns) ...
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11 views

statistically analyse pass rate of test in different locations

I'm looking to analyse some data and as it's been a long time since my statistics days I'd like to know which area of statistics my problem lies. Lets say I have a number of different driving ...
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Is there a measure of 'evenness' of spread?

I looked up on the web, but couldn't find anything helpful. I'm basically looking for a way to measure how 'evenly' a value is distributed. As in, an 'evenly' distributed distribution like X: and ...
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22 views

What kind of process is this?

For a k-steps stochastic process, assuming that it takes tk mins from the first step to reach the kth step. If we statistic the mean of cost time (tij) from ith step to jth step and the cost time ...
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11 views

Standard deviation of number of terms in a sum

If some random variables are drawn from a normal distribution N(m, s) with m > 0 until the sum of the draws exceeds some ...
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33 views

If the sample standard deviation and standard error are biased estimators, why are they still so useful?

The sample standard deviation and standard error of the mean are biased estimators for their corresponding population population parameters. As explained here for the sample standard deviation this is ...
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6 views

Calculate standard deviation bitween 2 group of numbers

i'm trying to figure the right way to do this. senario : i have 2 groups of number that represent seconds(if it's matter). Group 1 : 1 , 2 , 3 , 4 ground 2: 1.1 , 2.3 , 3.1 , 4,1 i need to know what ...
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Calculate standard deviation given tabled number of occurrences

I am going back through my old homework assignments to study for an upcoming Statistics test and one of the questions gives a table with number of children and number of women who have that number of ...
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How do I determine sample size to validate a requirement when I have a lot of margin?

I apologize if a similar question has been asked, but my search has yielded no results. I am having some trouble nailing down the correct methodology to use to design an experiment I am working on. ...
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25 views

Calculate Sample Size with VERY small standard deviation

I am facing a problem trying to estimate sample size for an A/B website test I am currently running trying to investigate difference in revenue per click per day (RPVD). Unfortunately, this metric ...
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28 views

When comparing variability between unequal samples, is there a way to correct for sample size?

I am trying to compare test measurements taken at three time points in a training paradigm. The data for each test consists of a number of durations in ms. The variable I'm interested in is the ...
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19 views

Cannot intuitively grasp “Standard normal deviate”

I cannot intuitively grasp the meaning of "Standard normal deviates". I think It would help if you provided me with either/all of the following: (i) real life examples of their application, (ii) an ...
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Can we use leave one out mean and standard deviation to reveal the outliers?

Suppose I have normally distributed data. For each element of the data I want to check how many SDs it is away from the mean. There might be an outlier in the data (likely only one, but might be also ...
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28 views

nls standard deviation calculation

I have fitted a non linear assymptotic equation to a set of data and my interest is in getting the standard deviations of the fitted parameters. Is this possible in nls?
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19 views

how to create such Z-score chart

I have a Z-score chart but I don't know how to create a similar chart. How can I create such Z-score chart?
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Why is permutation test wrong with variance but correct with standard deviation?

I am trying to understand the limits of permutation testing. I wrote up a small permutation test example in R, and found that permutation testing seems to fail when using absolute difference in ...
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20 views

Compare 2 RMSE with different Standard Deviation

How can I compare RMSE of two models with different SD. for example I have two models 1) RMSE=3.5 , SD=6.58, and 2) RMSE=17 , SD=28, how can compare these models. thanks
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Is it possible to manually calculate standard deviation for a multiply-imputed survey variable based on the standard error (SE)?

I am analyzing a multiply-imputed complex sample survey data using Stata. For normally distributed numerical variables I want to report the mean and standard deviation. However, the Stata command for ...
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35 views

Cumulative standard deviation of variables with different distribution

Suppose we have a set of basketball players, each of which have 9 associated performance categories. Each of these categories has a different distribution. I want to find a good way to represent how ...
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44 views

Distribution of the average of a sample of standard deviations

I have a sample of standard deviations. How is its average distributed? The sample is not big so normality is hardly possible. A.B.
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29 views

Standard Deviation and Variance

Can someone help me with this question because I'm not sure of how to do it exactly: There are two routes for a worker to get to his office. Both the routes involve hold ups due to traffic ...
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72 views

Badidas and Nikit Shoes

Good day everyone, I am self studying statistics at home and in the office whenever i have time. I want to improve my reporting. So i just came across this website and decided to try if could ask a ...
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How do I use the data from a full sample to inform my estimates about a subgroup?

Consider a sample of size $N$ with various observed characteristics: for example, gender and blood pressure. For the overall sample we have the average $\mu$ and standard deviation $\sigma$ of blood ...
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126 views

Comparing Standard Deviations with Different Units

Given: the standard deviation is 15.5 cents per gallon in one set of quoted prices and a standard deviation of $5.5 per barrel in another set of quoted prices. There are 33.5 gallons in 1 barrel. ...
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Using Bootstrap to estimate confidence interval of the standard deviation

I am trying to compare two different methods of estimating confidence intervals: a parametric approach that uses the assumption that the sample is t-distributed (i.e. the formulas that are given here: ...