# 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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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 ... 2answers 34 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 ... 0answers 19 views ### 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 ... 2answers 42 views ### 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 ... 0answers 16 views ### 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 ... 1answer 26 views ### 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 ... 3answers 56 views ### 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 ... 1answer 38 views ### 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 ... 0answers 19 views ### 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. ... 1answer 35 views ### 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 ... 0answers 32 views ### 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 ... 0answers 14 views ### 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 ... 0answers 19 views ### 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) + ... + ... 1answer 28 views ### 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 ... 2answers 39 views ### 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 ... 2answers 27 views ### 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? 1answer 25 views ### 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 ... 1answer 40 views ### 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 ... 1answer 14 views ### 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: ... 1answer 30 views ### 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 ... 0answers 26 views ### 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]: std dev = sqrt [(B - A^2/N)/N] ... 1answer 9 views ### 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: ... 0answers 27 views ### 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 ... 0answers 25 views ### 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. ... 1answer 22 views ### 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 ... 0answers 39 views ### 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 ... 0answers 14 views ### 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: $$F(x^{j}) = \frac{\sum^c_{k=1} n_k(\mu^j_k - \mu^j)^2{}} {\sum^c_{k=1}n_k(\sigma^j_k)^2}... 2answers 47 views ### Formula to recalculate Variance after removing a value and adding another one given old variance Let's say I have a data set of 10,20,30. My mean and variance here are mean= 20 and variance = 66.667. Is there a formula that lets me calculate the new variance value if I was to remove 10 ... 0answers 16 views ### Implication of ± 2 standard deviation I am currently taking a statistics class where we are studying about Standard Deviation. Even though it is a new concept for me still I am able to grasp it fairly quickly. But, we discussed something ... 0answers 10 views ### Calculating the standard deviation of calculated values that have uncertainty I am performing tensile testing and for each sample I test, the yield strength is determined by (yield stress) = (yield load) / (original area). The load and area have uncertainties associated with ... 1answer 18 views ### Standard deviation - use z-score to determine how the student placed comparing with the class average? A student took a math exam and scored 77. If the class exam scores were mound-shaped with a mean score of 70 and standard deviation of 16, use z-score to determine how the student placed comparing ... 1answer 27 views ### Binomial distribution with mean and standard deviation Can anyone help me with homework? I can`t catch a basic idea of the next exercise:$$ X\thicksim Bin(20,0.2)\\P(|X-\mu|\le\sigma)=?$$Can anyone at least explain how it opens,please? 1answer 57 views ### 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..... 0answers 35 views ### 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 ... 1answer 54 views ### 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 ... 1answer 49 views ### 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 ... 1answer 18 views ### 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 ... 1answer 15 views ### 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, ...