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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Covariance greater than Variance?

It is straightforward to verify that for two random variables $X$ and $Y$ with variances $\sigma^2_X \neq \sigma^2_Y$, we have that $$\Big|{\rm Cov}(X, Y)\Big| \leq \max\{\sigma^2_X,\, \sigma^2_Y\}$$ ...
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25 views

Find new mean from Normal probability

I have a problem as follows. Life of tyres normally distributed for a specific make. mean=24,000 km and sd= 2500 km. Question is: As a result of improvements in manufacture, the length of life is ...
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35 views

High variability in data set, how to normalize? [closed]

For my research I'm doing FACS analysis on neutrophils isolated from venous blood. The blood is taken from different individuals each day so there is high variation in the results, resulting in a high ...
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1answer
43 views

Can covariance be derived from means and variances?

In treatment studies it is common to report multiple outcome measures from the same subjects. The treatment effects on these outcomes are typically correlated so this should be taken into account ...
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7 views

Coefficient of variation to identify unique groups across datasets

I have a dataset containing a number of normal and diseased samples, with log2 expression values for ~12k genes . both normal and diseased samples come from different patients and/or diseases and I ...
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1answer
41 views

Combining Standard Deviation

im trying to figure out how to combine two Standard deviations of two data sets. Iam calculating the mass. I have density and volume data each with there own SD. So Mass = Volume X density Example ...
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1answer
22 views

How to calculate the Standard Deviation of a set of Percentages

I would like to know how to calculate the standard deviation (SD) of a set of percentages. Let me explain better. Some students performed a test and I counted the number of right answers for each ...
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36 views

Bootstrapping with standard deviation, mean and autocorrelation

I found in the matlab examples a way to use mean and sd for bootstrapping: ...
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2answers
65 views

Is it possible to use SD instead of entropy?

While discussing about decision trees in class, my teacher touched upon the topic of entropy. I have understood the purpose of entropy (have not understood how the formula $H(X)= -\sum_{i}{p(x_i) \log ...
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1answer
84 views

Why is variance (instead of standard deviation) the default measure of information content in principal components?

The information content of principal components is almost always expressed as a variance (e.g., in scree plots or in statements like "the first three PCs contain 95% of the total data variance"). The ...
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29 views

Finding for constant in a standard deviation problem

Let $X_1, \ldots, X_n$ be sample observations. Show that for any constant $c$, $$ (n-1)s^2\le\sum(X_i-c)^2 $$ where $s$ is the standard deviation of the observations. My professor gave this ...
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1answer
64 views

What is the simple standard error for MCMC?

Simply put: suppose that we have observed $X=\left\{ X_{1},\ldots,X_{n}\right\}$. We then need to calculate some statistic $T$ using MCMC, using $M$ loops (By "loops" I mean the number of times the ...
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2answers
134 views

Are there any other distributions whose shapes can be determined by just the mean and the standard deviation?

For the normal distribution, With the mean, and the standard deviation, we know the shape of the specific normal distribution - that is, the center of it and how spread out it is. I wonder if there ...
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12 views

Calculating overall variability over multiple datasets

I am trying to determine a way to measure the consistency of transit hours performed by transportation providers over their entire portfolio of shipping routes. For example, if a company has 3 ...
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2answers
46 views

Standardize non-normal predictors before performing binomial GLMM using mean and sd?

I am planning to predict a binomial variable (1/0, a used point by an animal or point available to an animal in its range) using several continuous, distance-based predictor variables (distance to ...
2
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1answer
56 views

Is my sample homogeneous? [closed]

I have a sample of 110 values between 0 and 180. These represent total degrees in an arc, and I want to be able to figure out whether or not I have a widely variable sample of arc sizes or if I have a ...
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2answers
259 views

For which distributions is there a closed-form unbiased estimator for the standard deviation?

For the normal distribution, there is an unbiased estimator of the standard deviation given by: $$\hat{\sigma}_\text{unbiased} = \frac{\Gamma(\frac{n-1}{2})}{\Gamma(\frac{n}{2})} ...
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3answers
116 views

Which statistical test to use when comparing two ratios?

I have five independent experiments. In each experiment I record the intensity of sample A and sample B, then add these intensities together and calculate A and B as a proportion of the total. ...
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0answers
38 views

Understanding correlation between Multiple Intelligences (MI) and digital technology competency

I appreciate all the help I can get to help me understand. The research reported here is about whether there is a correlation between multiple intelligences (MI) and digital technology competencies. ...
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5 views

Calculate trending of content from multiple sources

I'm not fantastically mathematical so please excuse any mis steps. Let me start with what I'm trying to do: I have news sources, for example: A. Washington Post B. TechCrunch C. Krebs on Security ...
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15 views

Parameterizing deviation from average

I am seeking help in parameterizing a concept. For instance: "Interest in literature" may be higher for poorer book owners than book owners with higher income, given that book ownership is only 10% ...
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2answers
88 views

Median absolute deviation (MAD) and SD of different distributions

For normally distributed data, the standard deviation $\sigma$ and the median absolute deviation $\text{MAD}$ are related by: $\sigma=\Phi^{-1}(3/4)\cdot \text{MAD}\approx1.4826\cdot\text{MAD},$ ...
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97 views

How can I measure fluctuation?

For a certain product I have a data series with its price for each day over a long period of time (20 years). I want to investigate how the fluctuation of the price changes over the whole time. ...
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2answers
67 views

Finding out if your data belongs to normal distribution

Is there a way to find out if your data belongs to one or more (mixture) normal distributions? I probably could calculate what is the standard deviation of my data, but I'm not sure what else to do ...
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9 views

How to calculate standard deviation of Integrated Discriminant Improvement (IDI) for logistic regression?

I have a new and old model. According to the paper Evaluating the added predictive ability of a new marker by Pencina, I can get the standard deviation of estimate of IDI by getting ...
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1answer
47 views

Standard deviation of residuals from a linear regression

I've ran this linear regression: mtcars_lm <- lm(mpg ~ wt, mtcars) Lets say I observe a value of mpg that is 2 above the ...
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3answers
128 views

Standard deviation to describe variation in positively skewed data?

I'm wondering how useful the standard deviation is when applied to positively skewed data? The standard deviation implies that 68% of data will lie within one standard deviation of the mean, but ...
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40 views

Assessing which player “wins” a series of predictions

A group of friends makes predictions about the outcome of the elections and we would like to assess who's predictions are closer to the final "outcome". For example, Here is a table of predictions for ...
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26 views

Is it possible to get a standard deviation of a data set compared to a target value?

I am working on defining performance measures for manufacturing and one of the performance measures I am working on has to do with the production time. Basically, the company sends releases different ...
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1answer
34 views

How to calculate standard deviations/z-score given a confidence level

So, I'm a total statistics neophyte, and need to calculate the number of standard deviations/z-score based on a confidence level, in javascript. I have a table which provides some data: ...
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50 views

Find the radius of a cluster, given that its center is the average of the centers of two other clusters

I do not know if it is possible to find it, but I am using Kmeans clustering, and I am stuck to the following. In my implementation, I create with two different threads the following clusters: ...
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1answer
29 views

Using sample standard deviation to estimate the standard error

In single-sample hypothesis testing, we can collect a sample and test whether the mean of this sample might have been drawn from the same population as some hypothesised mean. We use the standard ...
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1answer
14 views

Standard Deviation on a 1-4 scale

In a feedback survey I am analyzing, questions were asked on a 1-4 scale, with 1 being the lowest score and 4 the highest. The survey had a population of 10 people. For one question the mean came out ...
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40 views

The mean and standard deviation of an Kernel Density Estimation

[I have crossed posted this from StackOverflow. Not sure if this is allowed, but maybe there is a Python answer, or maybe there is a good stats answer] I have fitted a ...
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1answer
126 views

Sampling distribution, mean, standard deviation of finite discrete uniform population

Given positive integers $a$ and $b$ ($b \leq a$), where $c$ is the set of all combinations of $a$ digit binary numbers, with $b$ 1's, and where $c_1$ is least significant bit, and $c_a$ is most ...
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28 views

meta-analysis, effect sizes for standard deviations

Is there any possibility to calculate effect sizes for the differences of standard deviations of two groups? (Is there any possibility to calculate the difference in the standard deviation between two ...
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7answers
380 views

How to judge if 5 point Likert scale data are normally distributed?

I have read that the t-test is used when the population is normally distributed. How can I determine if my data are normal given that I am using 5-point Likert scale with a sample size of 100? What ...
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1answer
71 views

Empirical Rule. Is it applicable/usable in this case?

So I ran in this problem: I have to test whether Empirical Rule is applicable. Proportions I got is 73%, 94,7% and 99.1% (within one, two and three standard deviations). I'm worried about 73%. This is ...
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1answer
32 views

Why is GARCH better?

I estimated Value at Risk of a portfolio using 10 years of daily data. The values of VaR I got by three methods is: ...
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22 views

How to calculate the standard deviation of a 'deviation from a moving average'?

This question was previously asked on the Quantitative Finance site (http://quant.stackexchange.com/questions/15649/how-to-calculate-the-standard-deviation-of-a-deviation-from-a-moving-average), but I ...
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54 views

Square root of number of counts vs standard deviation of the mean?

I'm doing an experiment in radioactivity, where I measure the number of counts in a given time interval when a radioactive source is placed in front of a detector at a fixed distance. I repeat 3 times ...
2
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1answer
83 views

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 ...
2
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1answer
23 views

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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48 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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16 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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0answers
20 views

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 ...
2
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1answer
199 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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20 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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16 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 ...