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Questions tagged [standard-deviation]

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. Use this tag alongside (statistics).

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Norm 2 against norm inf

We know from basic linear algebra that $\forall x \neq 0, \frac{||x||_2}{||x||_{\infty}} \leq \sqrt{n}$ (where $n$ is the dimension).We also know that the equality occurs if and only if all ...
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Determining if 2 variances are equal with a rule of thumb?

So yes I am familiar with the F-test and know how to use it. Though I remember there was a quick rule of thumb of determine if 2 variances are equal. By either subtracting or dividing the 2 and it ...
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Back calculate X1 from standard deviation and X2 [closed]

I'm trying to calculate $X_1$ from a given standard deviation of population and $X_2$. The population is only $X_1$ and $X_2$. This seems like a simple rearrangement of the formula, but I can't get ...
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Standard deviation and variance (Check my work)

I got this question incorrect in an assignment. I have been through this again and come to the same answer. Can someone tell me where i went wrong please??
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Number of observations falling in a given criteria if mean and standard deviation are given.

This is a question from an entrance test. I was trying to solve it but now, i am stuck in it. Question is : If a data set is approximately normal with sample mean of 75 and standard deviation of ...
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Confused about standard deviation.

I'm a first year A level student studing maths, further maths, biology and chemistry. In maths, we find the standard deviation by dividing by n. In biolgy, we find the standard deviation by dividing ...
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What is the relation between standard error and power, and unequal randomization?

If you are doing some kind of hypothesis testing (superiority or equivalence) for the difference of two means/proportions, the standard error is: Square root of (Standard deviation of sample A / nA + ...
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Standard error arima/garch model

I have estimated an ARIMA/GARCH model. Now, I want to estimate the standard deviation, but I have multiple parameters. How can I do that? Thank you
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Crossover trials standard deviation/error

Hello, would anyone be able to explain how to get the standard deviation/error using this data? It’s supposedly 0.843 but I’m unsure as to how to get it. Many thanks in advance
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Edexcel A Level Statistics and Mechanics Year 1/AS Ex. 2E p.33 Q8 mean/standard deviation

I agree with the answer to (a). The problem I have is that if the answer to (c) is correct, then the mean would be (4+17)/2 = 10.5kn, which is different from the value 8.1kn from part (a), so ...
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Angle between regression line and SD line when plots flipped

The question I am working on is: The scatterplot y* vs x* has a regression line that makes an angle with SD line. Then the corresponding angle for the scatterplot of x* vs y* is: I have generated ...
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Standard Normal Distribution - the mean profit [closed]

The life of a certain type of car battery is known to be normally distributed with mean $30$ months and standard deviation $6$ months. The batteries cost the manufacturer $\$40$ each to make, and ...
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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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Difference between two standard deviation formulas

I was just wondering about the difference between these two standard deviation formulas? I am extremely confused because with one of the standard deviation formulas, it also requires the standard ...
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Mean of means and standard deviation

I have a set of data with their means $\mu_1,\mu_2,\ldots\mu_n$ and standard deviations $\sigma_1,\sigma_2,\ldots,\sigma_n$. These values refer to repetitions of the same experiment. How do I ...
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Standard error of estimation - Statistics

I have 2 sets of data X and Y for results of an exam. X - [some random exam result for exam x] - Number of data for x is 110 Y - [some random exam result for exam y] - Number of data for y is 130 ...
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Can I assume this data will be normally distributed?

If I were to get a sample of random people to solve a Sudoku puzzle, recording the time is takes them to complete it, can I model the range of times as a normal distribution with a mean $\mu$ and ...
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Standard Deviation of product of two Gaussian Distribution

If we have, $Z = XY,$ where $X$ and $Y$ have Gaussian Distribtuion, and both are independent. I solved with the Monte Carlo Algorithm, it shows some values of Standard Deviation, but I don't know ...
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Can the standard deviation change if the entire dataset is replicated?

Let's say I have a dataset : { a, b, c, d, e }. I calculate the standard deviation of the set and name it S. If I replicate ...
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How to get the Standard Deviation based on the sample

The situation is I have 96 sets of paper, 22 questions categorized into 5 categories.Every options consisting marks of 0,1,2,3,4. ...
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1answer
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Finding the probability that each apple in a randomly selected bag has a mass less than 105 grams.

I am practising normal distribution exam type questions but I am stuck at this one: The masses of individual apples sold in a food store are normally distributed. The supplier who provides the ...
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I need help in this statistics problem. Can somebody help?

So I have this raw data for a case study: Note: 1 stands for average weight and 2 for overweight. I need to calculate the following: What is the mean expected time spent for the average-weight ...
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number of times an experiment has to be repeated for optimal mean

I am trying to get the total execution time of a program - running it different times will give different run times since it depends on a lot of factors. Thus, I am running this program multiple times ...
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Standard Deviation of Values Raised to a Power

I have a question about finding the standard deviation of data raised to a power. Lets say we have n values: a_1, ... , a_n I put these n values through a softmax, thus: Let s = exp(a_1) + ... + ...
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Unbiased estimator of the standard deviation of the proportion

For the sample proportion $\hat{p}$, standard error is known as $\sqrt\frac{\hat{p}(1-\hat{p})}{n}$. I wonder whether this is the unbiased estimator for the standard deviation of the sample ...
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Why is the standard deviation important for non-normal distributions?

In the case of the normal distribution, I know that the standard deviation tells me that 78% of my sample is in the interval $[\mu - \sigma, \mu + \sigma]$. Suppose I have another sample which is not ...
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IQR , standard deviation

there is a a sample such that the standard deviation is significantly smaller than IQR? I think that no but how to prove this?
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Can two standard deviation be a negative number?

Given a simple data set, the two standard deviation is calculated as a negative number. Shouldn't the standard deviations (min or max) be within the range of the data set? My data set: 2 31 32 22 ...
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Estimating the standard deviation based on sample

I have been given a problem for homework with which I need a little help. In part A, I suspect that the solution has to do something with the degrees of freedom where we use n-1 for sample and n for ...
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1answer
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two definition of variance identity

$I_n$ is the indicator rv where $I_n=1$ if $A_n$ occurs and 0 otherwise. Then define $\eta_n = \sum_{k=1}^n I_k$ I'm given this statement: But in another post about the same proof, I have this: ...
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The value of p in a Standard deviation of a binomial Distribution

The random variable $X$ has a binomial distribution $b(n,p)$. For what value of $p$ is the standard deviation of $X$ the greatest (note: the answer is independent of $n$). Can someone help with ...
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computing standard deviation without mean produces illegal result! [closed]

I would like to compute STD in one-pass, without first computing the mean: Hence, I decided to use the following [formula][1]: std dev = sqrt [(B - A^2/N)/N] ...
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Standard Deviation of pre/post test scores

I have a problem that I need help with, please! I have results of a pre/post test and I was asked to find the standard deviation for that particular question. Here is what the output looks like: ...
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What does x represent in this question?

I am confused how did they end up with $X = 3000, -9700$ shouldnt it be $X = 100000 , 9700$ as it will represent the payment without premium and with premium? I am really finding difficulty in ...
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What is the minimum variance band of Poisson Distribution?

I am trying to calculate the minimum variance bound of Poisson Distribution. poisson distribution: P(X=x)=(λ^x)/x! e^-λ, were λ is the mean. I got λ/(sum of x), but I am not sure if this is right. ...
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Overall standard deviation of two groups without data points?

$15$ boys: mean of $47.6$, standard deviation of $11.2$. $10$ girls: mean of $49.1$, standard deviation of $15.4$. Overall standard deviation of the marks? How would I go about accurately finding the ...
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Doubts regarding Central Limit Theorem

All, I am studying CLT and I had a doubt. I understand that sampling distribution has a mean same as population mean and std.dev as 6/sqrt(n) where n is sample size. Each point on X axis of ...
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Standard deviation of k-th class, corresponding to j-th feature

I'm trying to calculate Fisher's score for a feature from a data set. The fisher score for the $j$-th feature: $$F(x^{j}) = \frac{\sum^c_{k=1} n_k(\mu^j_k - \mu^j)^2{}} {\sum^c_{k=1}n_k(\sigma^j_k)^2}...
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Formula to recalculate Variance after removing a value and adding another one given old variance

Let's say I have a data set of $10,20,30$. My mean and variance here are mean= $20$ and variance = $66.667$. Is there a formula that lets me calculate the new variance value if I was to remove $10$ ...
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Implication of ± 2 standard deviation

I am currently taking a statistics class where we are studying about Standard Deviation. Even though it is a new concept for me still I am able to grasp it fairly quickly. But, we discussed something ...
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Calculating the standard deviation of calculated values that have uncertainty

I am performing tensile testing and for each sample I test, the yield strength is determined by (yield stress) = (yield load) / (original area). The load and area have uncertainties associated with ...
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Standard deviation - use z-score to determine how the student placed comparing with the class average?

A student took a math exam and scored 77. If the class exam scores were mound-shaped with a mean score of 70 and standard deviation of 16, use z-score to determine how the student placed comparing ...
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Binomial distribution with mean and standard deviation

Can anyone help me with homework? I can`t catch a basic idea of the next exercise: $$ X\thicksim Bin(20,0.2)\\P(|X-\mu|\le\sigma)=? $$ Can anyone at least explain how it opens,please?
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Drawing random realisation from quantity with poisson error

How would I draw a random realisation of a variable with an upper and lower error determined from Poisson statistics using the Gehrels 1986 formula? See: http://adsabs.harvard.edu/abs/1986ApJ...303.....
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Find the Probable Error.

Hi guys I've been studying statistics these days and found a problem that really got me confused, since I really don't know or seem to find any clue to work out the problem, the problem says the ...
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1answer
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How to proof variance of the sum $x+y$ is the sum of variance $\sigma_x^2$ of $x$ and the variance $\sigma_y^2$ of $y$?

Show that the variance of the sum $x + y$ of the random variable $x$ and the random variable $y$ is the sum of the variance $\sigma_x^2$ of $x$ and the variance $\sigma_y^2$ of $y$? My attempt: Is ...
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Efficient computation of incremental standard deviation (removing first value)

I found this link about incremental standard deviation where it computes the standard deviation every time a new element was added to the dataset. Is there a similar method when adding a new value ...
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1answer
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Relationship between the standard error of the estimators and the standard error of the error term [closed]

I'm trying to solve the following problem: My thinking is that If the Standard error of the error term would then the error term of the regression would also fall (as the regression would start ...
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How do I find the $z-score of something when not given an x?

I'm given a mean and a standard deviation. The question asks: How much chicken do you have to eat in order to be in the top $5%$ of everyone else. Mean = $55$ Standard Deviation $=9.2$ The answer ...
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Is standard deviation defiined for Hamming norm

Is there a way to define the concept of standard deviation for binary norms like Hamming norm? For two words (in most general case - sequences of symbols from a given alphabet) of the same length, ...