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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Comparison of dispersion measures of different samples with different subsamples

Context: I have data on movie ratings and I want to find what factors affect the rating the most. I have $k$ features $F_1, F_2,\ldots,F_k$ characterizing a movie - for example, director, lead actor, ...
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Decreases in the estimated standard deviation have what effect on required sample size? [closed]

Decreases in the estimated standard deviation have what effect on required sample size? Multiple Choice: Increases. Decreases. No effect. Indeterminate.
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Test to see if data is close to zero

I'd like to test if my data is close to zero. I can take the mean but I also want the standard deviation to be small. Is there a statistical test that produces a single number to quantify this? For ...
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Can IQR ever be larger than standard deviation?

As I understand it the IQR specifies the dispersion of the data by taking the difference between Q3 and Q1 (i.e., the range that the middle 50% of the data lies), while std specifies dispersion using ...
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Detect swing high and low in set of price [duplicate]

I have set of prices which when plotted in line graph looks somewhat like this , How do I find the prices in the place where I marked red arrow. Any algorithmic/mathematical Idea will be really ...
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Calculating calm market [closed]

I want to find when the market is calm. By calm I mean that it shouldn't go up or down. Instead, it should stay inline or close to inline. For this reason, I'm trying to calculate the standard ...
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Can you infer standard deviation/error from bootstrapped confidence intervals?

I've got the summary of a data set, but not the actual data. They've calculated confidence intervals using bootstrapping. I know the sample size, so if they were normally calculated confidence ...
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What is the difference between population standard deviation, sample standard deviation, and standard error?

Sorry for the rudimentary question, but I just want to make sure I understand everything well conceptually. I understand how we get the standard deviation of a population. My questions are as follows: ...
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Understand the standard deviation

This is definitely a very basic question but it is something which is in my head for some time now as I struggle to get the real meaning or sense of the standard deviation. How to apply it is not ...
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How to rescale predicted standard deviation values of scikit-learn's GP module to get the actual std values?

I am using scikit-learn's Gaussian Process Regression module to model some data. The issue with my data is that I cannot Normalize my data since I don't know the exact bounds of my data: the minimum ...
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Combining independent experiments each one with mean and std desv

This might be already asked and answered. However, all the questions and answers for possible similar questions are too high level for me. So, I will generate a very simple example and please, do ...
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Does Standard Deviation Increase/Decrease when Average Increases?

I have a mean(88) and standard deviation(6) of sample data from period 1, I have the mean(91) for period 2 data; the mean increases from period 1 to period 2. Additionally, I have sample data from ...
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Which one is correct presentation for descriptive statistic of a transformed variable between retransformed mean (estimated SD), and median (qurtiles)

If a collected variable has a skewed distribution toward one side and transformed for statistical analysis, which one is better for descriptive statistics presentation between re-transformed mean and ...
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Why Standard deviation formula has n-1 in the denominator but Variance only n? [duplicate]

If is true that SQRT(Variance) = SD then one cannot have n-1 in the denominator and the other not but should be same? SD formula: Variance formula:
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Calculate standard deviation for percent change from baseline of mean difference between groups

I have data from a study that compares two treatments for lowering plasma cholesterol. The data is reported as mean cholesterol before and after the intervention with their associated SD. The ...
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Question about the use of the word “standard error” in several situations

I'm now reading the book Computer Age Statistical Inference and I'm not sure what the standard error actually refers to in several cases. In Page 9, the author defines for two data sets AML and ALL (...
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Standard Deviation from population and only a percentage of the sample

I have found this formula in a help file in a program I have for statistical significance. s = standard deviation p = result in percentage n = size of sample I'm trying to validate and understand ...
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Exponential moving average before computing std

In which cases it would make sense to use exponentially weighted moving average (EWMA) before, for example, computing sample variance or other statistical analysis? Could you give an example when one ...
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Impact of standard deviation that is caused by a new variable

Assume you have a distribution. {X1,X2,X3 .......Xn} For this distribution SD can be say, 50. We introduce a new variable or a sample item to this distribution. Say Xn+1 Now SD could change. For ...
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Sample Variance and Dividing by $n-1$

In this video... https://www.youtube.com/watch?v=sHRBg6BhKjI ...and in many others, the explanation for why when calculating the sample variance we divide by $n-1$ instead of by $n$ is the following:...
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Relationship between measurement precision and the precision of the mean of repeated measurements [closed]

Measurement precision can be improved by measuring the same quantity multiple times and taking the average. In other words, the average of several measurements of the same thing is more likely to be ...
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How to calculate the precision of the mean of univariate time series data, based on the precision of the discrete measurements it consists of?

Assume that the precision of the measurements is fixed and independent – each discrete measurement has the same degree of random error, and is independent of all other measurements. For example, ...
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Calculating employee performance via standard deviations from the mean per day, averaged to larger timeframes

I have a dataset that includes performance of employees on various projects, day by day. The dataset has hours worked for the day, and number of widgets created that day. We're interested in looking ...
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Standard deviation formula

I faced the below formula for standard deviation. Is it correct or no? If it is How can I simplify or expand it. $$ \sigma(S) \ = \sum_{s \in S} \frac{s^2}{|S|} - avg(S)^2 $$
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If the coefficient of determination is a measure based on variance, then what about standard deviation instead?

Background: I've been teaching a very simple course of introductory Statistics for a few years now and we cover linear correlation and the Correlation Coefficient ($r$). I want to introduce the ...
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Show that if $Y$ has $E(Y)=μ,Var(Y)=σ^2$, and $P(|Y-μ|<σ)=0$, then $Y$ has the same distribution as $X$ described below for $k=1$

I'm having a hard time proving the second and third case of $X$: Show that if $Y$ has $E(Y)=μ,Var(Y)=σ^2$, and $P(|Y-μ|<σ)=0$, then $Y$ has the same distribution as $X$ described below for $k=1$. $...
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Find the expected value of the sample mean

A fair four-sided die with four equilateral triangle-shaped faces is tossed 200 times. Each of the die's four faces shows a different number from 1 to 4. (a) Find the expected value of the sample ...
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calculating standard deviation with a previous calculation and a delta

I have a large amount of data for which I have got a system that has calculated the standard deviation. I can augment this data when doing the calculation. Such as also calculating the mean and ...
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Maximum Likelihood with Experimental Data: Standard Errors and Standard Deviations

Suppose we have a set of experimental data $\{(x_i, Y_i, S_i)\}_{i=1}^N$ where the $x_i$'s are our measurement points, the $Y_i$'s are the mean value of the response $y$ over $m$ experiments at $x_i$, ...
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How does standard deviation error change/improve as I average more measurements?

Let's say I can measure something with a know standard deviation of $\sigma$. Let's say I measure it $n$ times and take the mean of the $n$ measurements to determine a more accurate mean value. What ...
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Relationship between expected absolute deviation and standard deviation

The standard deviation of a random variable $X$, $$\sigma = \sqrt{Var[{X}]} = \sqrt{E[X^2 - E[X]^2]}$$ is a very commonly used measure of "normal" distance from the mean of $X$. A much less frequently ...
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Comparing standard errors obtained from error analysis to calculated values

Say I have completed some error analysis on a function and determined that the error in a particular variable ought to be ± 0.05 m for a particular variable. If I had a dataset of measurements made of ...
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What does the root mean square difference tell me that the mean difference doesn't?

If I have the below data and my difference measure is "actual/extrapolated-1" for the same observation. What does the RMSD tell me that the mean difference doesn't? If I understand the 'mean ...
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No effect by sd parameter in arima.sim model parameter

I am new to R. I wanted to create an ARIMA(1,0,0) model which simulates data with the coefficient been 0.1. I used the following code: ...
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1answer
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All readings are within one sigma. What does this mean?

A basic question from a novice to statistical concepts. I am doing a small test wherein I measured a 100 observations of a same reading to check for the repeatability of the measurement data. On ...
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Question About Semi-interquartile Range

So I have a homework question that I'm stuck on. Part A asks: Explain why you cannot calculate the semi-interquartile range if you know only the difference between either Q3 and the median or the ...
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How would I calculate the standardized value of y given the standardized value of x and

If the correlation between two variables, $x$ and $y$, is $-1/2$, and the standardized value of $x$ is $-4$, how would I predict the standardized value of $y$ with just those two pieces of information?...
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How would I calculate the standard deviation of a sample given the sample size, mean, and sum of the data's squares?

For example, given: $\sum_{i=1}^n x_i^2 = 10$, $n=10$, and $mean = 10$, how would I go about calculating the standard deviation? The formula for standard deviation requires me knowing what $\sum_{i=1}^...
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Outlier removal, extremes on both ends

A list of numbers and I want to remove the extremes on both ends. The standard deviation is calculated: 26.3 (rounded to 1 decimal) ...
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Deviation Coding meaning of test statistic on grand mean (intercept)

I have a dataset with 7 factor levels none of which are a reasonable reference group, so I've chosen to set up my GLM (negative binomial) analysis using deviation coding. I've studied this question ...
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Back-calculation of the minimum sample size for an mechanical experiment

I want to back-calculate the minimum sample size for an experiment. I have a known mean and standard variance of a statistical population. From the statistical population I chose two samples with ...
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Convert median absolute deviation (MAD) to SD for log-normal distribution

How do I convert the $\text{MAD}$ (median absolute deviation from the median) of data that is drawn from a log-normal distribution to the standard deviation of a log-normal distribution? To clarify, ...
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What distribution can be predicted more accurately?

I am working on simple statistical prediction. However, whatever i did, i come up with a high range. I have used standard deviation and also percentile. Yes they work well in the given data but the ...
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How to find probability of quantiles given mean and variance? [closed]

If someone could explain the process for beginning this and the formulas involved I would be grateful. Male height in the Netherlands is normally distributed with a mean of 73 inches and a ...
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1answer
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Is this logic correct regarding how standard deviations work with a simple game example? [closed]

Say we have a game where you start at 0 points, you are allowed to get negative points per round and allowed to have negative total points. The points you earn each round is on average 1 with a ...
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Will changing the standard deviation affect the distribution?

Let's say I want to generate some random data that follows the normal distribution, with a mean of 5. Will setting the standard deviation to 3 or 5 affect the distribution, that is, will it still ...
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When to use Bessel correction and and does it alter the standard error?

is there any condition about when to use the Bessel correction as Python uses it to find the Standard Deviation by default. The standard error of the mean is $\...
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accuracy of the mean

I am doing a study on the performance of Aquifer thermal energy storage systems. During this study, I get results with consist of a normal distribution around a mean. What can I now say about the ...
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Estimate standard deviation of responses from ANOVA

I've created an ANOVA table, but I'm being asked to estimate the standard deviation of responses based on this ANOVA table. I haven't been able to find any sort of formula anywhere about how to ...
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Is it possible to get equivalences of Western Electric Rules in non normal distribution with percentile values?

I am not a statistician and I am a bit lost with these concepts, but I will try to explain my situation. I have a non-normally distributed data, and I am trying to apply the Western Electric Rules to ...