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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Unstandardize z score values that have mu and standard deviation of 0 and 1 respectively

Is it possible for one to unstandardize z score values with mean 0 and standard deviation of 1 back to its original value, given that the mean and standard deviation of the original data is not ...
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Discrete correlation function (sample cross-covariance)

The continuous correlation function for the random variable $A(t)$ at a instant of time $t$ is given by \begin{equation} C_{AA}(\tau) =\frac{1}{T} \int_{0}^T d\bar{t} A(\bar{t})A(\bar{t}+\tau) \end{...
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Does PCA normalize data with respect to standard deviation?

In my textbook it says the data is assumed to be zero-centered. I am not sure what this means. I read it stand for substracting the mean from the individual values, however I would like to know do you ...
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Including descriptive statistics as regressor in a panel model

I have panel data and believe that independent variable X drives changes in Y. However, my hypothesis is that the relationship between X and Y is modified by the volatility of X. Generally speaking, ...
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What is the statistical efficiency of the sample standard deviation?

I've been reading about measures of scale and data dispersion, and often come across the term statistical efficiency, which is used as a means of comparison (as well as breakdown points), of different ...
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Standard deviation of truncated uniform and gaussian distributions?

I'm dealing with 2 data vectors $A$ and $B$, that, after some processing, need to be truncated (or rectified, not sure what the correct term is), i.e., $A_{trunc} = abs(A),$ and $B_{trunc} = abs(B)$. $...
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Find range of values 95% of the time for a weighted sample

I want to generate some data about a new game I am playing. There exists a mechanic in the game where you can critically strike, dealing extra damage. You can also deal different amounts of damage in ...
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Derive standard deviation from mean, sample size and 95% CI

I am planning a clinical study and need to determine the needed sample size. My primary endpoint will be measured in blood pressure (mmHg). Many studies already exist for this, but they do not often ...
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Which Standard Deviation do I use when calculating the R squared of a Holdout Sample?

When I am calculating the accuracy of my regression model on my holdout sample, which standard deviation do I use? Currently, I am using this formula: R squared = 1 - (sum(holdout - predicted)^2) / ((...
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How to get the “reliability percentage” of a measurement

I need to get the amount of confidence I can have on a measurement (from 0 to 100 percent). In other words, I need to know how much reliable the data on a measurement is for me to trust its ...
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How to calculate the range from mean and SD?

Is is possible to calculate or estimate the range of a population if I know the mean, population size and standard deviation? I am doing a research and the mean age of the population is 29.9 +/- 5.3 ...
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Standard deviation and confidence interval

How do I calculate/obtain the standard deviation and confidence interval with the information below? For example, to obtain a base case utility value of 0.715, the following equation is used with the ...
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What is the mean absolute difference between values in a normal distribution?

I understand that variance is mean of squared differences and that standard deviation is square root of the mean. What, however, is the average difference between values in a normal distribution (...
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How can I estimate the distribution of sizes if I sample from the tails of that distribution?

Let’s say I have an insect farm and they lay down a lot of eggs, which I collect in a cup. Now I want to study the size distribution of those eggs, but there’s a problem: The younger eggs, which are ...
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Time series forecast where each measurment is already averaged and has a spread

I would like to forecast a time series consisting of time averaged (everything happening during 15min intervals is averaged and recorded with a timestamp of the start of messurment) quantities (...
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Should an observation always belong to the population to calculate its z-score?

It was mentioned in this link that, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value ...
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Confidence intervals for a joint probability distribution [duplicate]

I've asked this question before but it was marked as a duplicate with this question that didn't answer my question. My question is as follows: I have a 2-D probability distribution along the lines of ...
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Generalizing variance to two dimensions [duplicate]

I have a 2-D probability distribution along the lines of this plot: I know how to find the confidence interval for a 1-D probability distribution (by the definition of standard deviation or the 68-95-...
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How do you compare standard deviations?

For example, if I am a scientist evaluating 2 methods to determine blood glucose and I want to compare if one is more variable, I would take, say, 6 samples from each person (subject) and use Method A ...
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Need help understanding Bernoulli standard deviation

I'm looking at the solution of a homework problem from a class I took many years ago and I'm not understanding how they calculated standard deviation (see question 1C here: http://datasciencelabs....
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Understanding Standard Deviation for non-normally distributed data [duplicate]

On a normal distribution curve, standard deviation tells us how much data fall in each group around the mean, according to empirical law. So, for example of SD = 14 and sample mean($\bar{x}$) = 50, as ...
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Determine whether an error is random?

We have two measurements of the temperature of the same object as: $T_1 = 46 \pm 2 F$ and $T_2 = 58 \pm 6 F$. Normally, the agreement between the measurements could shown to a standard deviation by ...
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How to find margin of error for 99% confidence interval for skewed distribution?

Google Sheet of data I have the value and the frequency of the data. As you can see in the data sheet, the count number is quite high, so I am not able to write out the entire list of the data (ex. 2, ...
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How to simulate standard deviation

I would like to simulate data based on real data captured. The real data captured is 15 observations. The simulation based on the existing data is 100 observations. I have a mean and standard ...
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Standard Deviation of Bernoulli trials / Bernoulli process with different probabilities

If 20 independent Bernoulli trials are carried out each with a different probability of success and therefore failure, what is the standard deviation of the result? How is this calculated?
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Same mean but different standard deviation, how to interpret?

Can i just assume they have the same behavior? i need some advice on how i would look at these graphs. Should I use standard deviation to analyse fluctuation or median instead of mean? or can i just ...
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How to interpret two graphs/data with the same mean but different standard deviation?

I have two lines with the same average, but has more fluctuation, do i analyse them in the same way and make conclusion? Basically i need some advice on how i would look at these graphs. Should I use ...
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Confused when to use Population vs Sample standard deviation in engineering testing

When I run an test for something (say 10 trials) and want to find the standard deviation of all 10 trials, I am getting confused if I should use the sample or population standard deviation. My initial ...
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K-Fold Cross-Validation - Formula for Standard Errors

I've recently tried to understand and formalize the one-standard-error rule for model selection by means of cross-validation. However, unfortunately I found most of the descriptions of the CV standard ...
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CLT - Adding small samples to one big sample

According to CLT, the SE is the SD of the distribution of several samples means. This SE depends on each sample mean, the SD of each sample and N (the size of each sample which I test). Since there ...
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Understanding RSE(Residual Standard Error)

I am reading the book " An Introduction to Statistical Learning " and I have trouble understanding their explanation of RSE(Residual Standard Error ) . This is what the book says : "The ...
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Data normalization by using mean and standard deviation - Strange example

I read a paper which talks about two samples; the first one concerning data (e.g. resistance $R_{ct}$) from a biosensor1 (called module), the second one concerning data from biosensor2 (called CHI). ...
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Standard error of model residual SD from simulation

I'm futzing with getting the SE of model residual standard deviations from a linear regression, and keep getting narrower errors than I should - and I'd like to figure out why. The basic approach I'm ...
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Why is the standard deviation for this data zero, and what does that imply?

I found the following data for 1000 rolls of a 20-sided die by a dice program: [38, 53, 47, 42, 58, 42, 47, 56, 48, 57, 49, 49, 47, 45, 43, 49, 52, 55, 62, 61] (...
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Compute means using number of observations and standard deviation

Is it possible to compute mean using standard deviation and number of observations?
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How to interpret standard deviations when comparing two variables (when taking log)?

I'm comparing two models, in one model I take the log of one of the independent variables (in the other I don't). I've compared R squared values, but I also want to compare the variables themselves. I ...
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Why isn't absolute deviation used [duplicate]

If the reason that standard deviation is used is that it's easier to just square the distance every time than find the absolute value. Then why is √(E(x-m)^2)/n not used because if I'm not mistaken |x|...
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Project estimate assumptions with PERT and confidence interval

I've read the Wikpedia article Three-Points Estimation and the book "Software Estimation" written by Steve McConnell. I globally grasped the process, however I have very little knowledge in ...
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PERT pessimistic formula and standard deviation

I've just read the book "Software Estimation" written by Steve McConnell. I have very little knowledge in statistics. The well known PERT formula to estimate the time of a task is: ...
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How can I calculate the mean and variance of a linearly transformed random variable?

Say I have a random variable $x$, with mean $\mu_x=35$ and standard deviation $\sigma_x=10$. I want to linearly transform $x$ to $y$ according to the formula $y=a+bx$ so that $\mu_y=100$ and $\sigma_y=...
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Calculating standard deviation without original measurements

Assume I have the monthly data for the price of items like this: num_items = [10, 22, 13, 4, 15] avg_cost = [200, 103, 143, 412, 123] Now, I do not have the original list of item-wise cost table. From ...
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Impact of unit conversion on the relationship between standard deviation and variance

What impact should unit conversion have on the relationship between standard deviation and variance? For example, when the units are kilograms, the sd is 3.156 kg , and the variance is 9.96 kg which ...
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rms: Calculation of standardised / studentised residuals from a lrm object

I would like to calculate standardised and studentised residuals from a logistic model fit using lrm from the rms package. ...
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Standard Error or Standard Deviation for error associated with averaging raster values within a polygon?

I am trying to measure uncertainty associated with a mean value for spatial data. I have: A polygon representing a spatial district. A raster dataset that was produced via a Random Forests model, ...
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What came first, the covariance or the correlation matrix?

Covariance can be calculated from correlation and correlation can be calculated from covariance. Is it sufficient to refer to them as only transformations of one another? Is one considered more of a ...
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How to reconcile z-scores into a number from -1 to 1? [duplicate]

I'm looking at time-series data of the GDP of the economy. I'm comparing the difference in the percent change of the GDP over the past 1 months, with the past 2 months — doing this over the course of ...
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How to reconcile z-scores into a number from -1 to 1?

I'm looking at time-series data of the GDP of the economy. I'm comparing the difference in the percent change of the GDP over the past 1 months, with the past 2 months — doing this over the course of ...
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Given two samples that have the same mean, standard deviation, and N: are the values in each sample identical?

If not, are there any restrictions that would need to be imposed to ensure that the values of the two samples would be identical? I apologize in advance if this is such a basic question.
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How to calculate p-value?

I'm looking at two sets of data: timestamps for some known events, and timestamps for events measured by an instrument. I want to determine whether that instrument is "seeing" those events. ...
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Standard deviation and confidence level: how to interpret and evaluate the results

Apologies if this may sounds a dumb question, but the more I'm trying to understand how to interpret and evaluate the results, the more I can't find a proper answer. I've been trying to understand the ...

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