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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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Variability calculation based on standard deviation

I need assistance with calculating the standard deviation for a list of items, where the monthly consumption needs over the past 12 months are detailed for each item. My objective is to classify these ...
Inbar Oz's user avatar
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Calculate standard deviation for difference of two populations

I have two populations, let's say $P_1$ and $P_2$, and they have their own standard deviations, like $STD_1$ and $STD_2$. From this populations I need to calculate which one is better. I do that by ...
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Computing error bars for the geometric mean across multiple datasets

I apologize because my understanding of statistics is somewhat basic. I will try to describe the problem as well as I can. My colleagues and I have a graph where we measure the relative performance of ...
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Calculate the uncertainty from the geometric mean and geometric standard deviation

I'm working on a database that provide for each entry a geometric mean value as well as a geometric standard deviation. I would like to transform this value into an approximate relative uncertainty. ...
Thibault Abry's user avatar
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Is the average distance from the average statistically meaningful?

Where this value is defined as $$\frac{1}{n} \cdot \sum_{i=1}^{n} |\overline{x} - x_i|$$ does it have any significance or use in statistics?
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Percentage of values between 3 standard deviations and 4 standard deviations.

After learning about the empirical rule / 68-95-99.7 rule, I am just wondering about the percentage of values 4 standard deviations from the mean. This question is pretty much the same as the ...
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Standard deviation in 3d space

Is there anything analogous to the standard deviation, but in three-dimensional space? I have two set of data SET A 3D coordinates point X Y Z a1 2.09 -1.2 4.03 b1 7.31 8.5 -2.8 c1 -3.45 1.12 9....
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Difference between grade averages of different graders

I am a teacher and we now had our end-of-semester exam in which $N$ students participated. I have $k$ graders each graded a certain amount of exams $N_i$, so $\sum_{i=1}^kN_i=N$. When I check the ...
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How to prove the inequality for the standard deviation of a linear combination of two random variables

The question comes from ‘Mathematics for Finance: An Introduction to Financial Engineering’ by Marek Capiński (Author), Tomasz Zastawniak. The book provides a conclusion about the risk and return of ...
bokabokaboka's user avatar
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Why does the standard deviation have all the properties it does? [closed]

Currently in a probability class and am having a hard time wrapping my head around the standard deviation. In many ways it feels "made up" to me; let me explain: $$\sqrt{a^2 + b^2} \neq a + ...
Renee Kim's user avatar
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How to calculate historical returns and variance for a single asset with non buy-and-hold strategy

Suppose i have a strategy that is not buy-and-hold type of strategy. It can have unique entry timing and unique exit timing for a single asset and both long, and short positions will be allowed, and ...
Kevin Kim's user avatar
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Generalization of Geometric Mean, Standard Deviation, etc.

The geometric mean can be thought of as the exponential of the arithmetic mean of the logarithms of your dataset $\{a_i\}_{i=1}^n$: $$GM = \exp\left(\dfrac{1}{n}\sum_{i=1}^{n}\ln(a_i)\right)$$ ...
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Standard deviation on Monte Carlo runs

I'm currently working on dynamic system identification and performing Monte Carlo runs with different noise realisations at a given $SNR$ ratio. Once the parameters converge, I save them in a matrix ...
Jean-Fr's user avatar
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Average is higher than 75th percentile [closed]

I have a statistical question with mean, median and percentile. I have run my data with over thousand samples. From this run, I can see that the Average result value is higher than the median and ...
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Taking partial derivative of SSD, wrt the parameters $a, b$?

In the book titled: Analysis of Straight-line data, by Forman S. Acton; it is given on page #10: The classical 'least squares' procedure is most commonly derived by forming an expression for the sum ...
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Why is the demonstration of the "sample" standard deviation somehow more exact than the classic standard deviation, if $\frac{x}{n} ≠ \frac{x}{n-1}$?

I cannot see why to use the "sample standard deviation" instead of the classic "standard deviation" (the "population") ever, most explanations I find are just prescribing ...
algo's user avatar
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Confusion with effect of averaging on standard deviation

First of all, I was reading a text and stuck with this part: Now regarding the above quote, I want to give two scenarios I made up to make my question clear: Scenario 1: Imagine we take N ...
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How do I get the sample deviation from population deviation when sampling is done without replacement from a finite population [closed]

How do I get the sample deviation from population deviation when sampling is done without replacement from a finite population? The deriving step by step was needed. enter image description here
Dunken Zhao's user avatar
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Lower bound on sample size to determine coin fairness

This is a conclusion I came to through very basic knowledge of statistics and error analysis. Suppose we want to determine the fairness of a coin. To do this, we need to determine the probability of ...
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How does the standard deviation change if you change one value?

Question: There are 23 employees in a particular division of a company. Their salaries have a mean of \$70,000, a median of \$55,000, and a standard deviation of \$20,000. The largest number on the ...
Ryan Wang's user avatar
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Finding weighted standard deviation

In short I have 2 columns of data; quantity and time taken for that quantity of items to get from point A to B. e.g. Quantity Travel time (Days) 725 10 583 12 609 11 23 2 447 13 14 28 I want ...
Ventsi Radev's user avatar
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Normalize data around a specific value

I am having trouble to solve a problem about normalization around a specific value. Let's say i have this data below: ValueA ValueB Division (A/B) Gap (Division - 0.625) 10 10 1 0.375 10 16 0.625 0 ...
romainL's user avatar
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Is there a relationship between the harmonic mean and the arithmetic standard deviation?

I was doing a thought experiment on the harmonic mean. Let's say we have a sequence of 4 numbers: 100, 110, 90, 100 The arithmetic mean (AM) of this sequence is 100 but the harmonic mean (HM) is 99....
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Estimation of std error using sample std dev. will result in diff. sample statistic distribution for diff. samples. Won't this affect our decision?

During hypothesis testing (say, comparison of sample mean to a hypothesised population mean), we calculate p-value using sample mean distribution. For constructing this sample mean distribution, we ...
Swapna Sarit's user avatar
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Comparing proportions inside groups...? [closed]

Let's say I wanted to compare the wealth of people in 2 groups to see in which one the wealth is distributed in a more progressively escalated manner: In group A we have 3 people: One with 12,000 $ ...
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How to calculate standard deviation (σ) for a real time (live) data?

This is a graph of live data. The red band is a 'VWAP' Volume weighted moving average. I want to calculate standard deviation (1σ) of that red line. I have used the formula (image attached), where 'M'...
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How is it Possible to Optimize the Shichman-Hodges Slope Parameters from the Left and Right using Least Square Linear Regression Approaches

The Shichman-Hodges equations model a curve that on the left-hand side has a slope that decreases as a function of the variable $x_i$. That is $x_0=0$, and $y_i$ is a function of $x_i$ for $i=0$, and ...
Stephen Elliott's user avatar
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Calculation of $\sigma_{\text{diff}}$ gives a complex number, indicating a potential error in variance computation

Given below is the problem I have solved but I am getting complex number as an answer for $\sigma_{\text{diff}}$ which is supposed to be real number. I need guidance. Have I made mistake in previous ...
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Average Deviation of Cards

Suppose we draw cards from a standard 52 card deck where each card has a value from 1-13 (Ace being 1 King being 13). What is the average deviation of the value of a randomly selected card? What is ...
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Constructing the MGF from the mean and Variance

If I have the mean, variance, PDF and CDF of a random variable $X$ how to easily construct the MGF.
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How can I calculate the SD from the SE of a least square mean?

I am conducting a meta-analysis and I need to collect mean and standard deviations (SDs). In some studies the raw means are not available and least square means are provided instead. Is there a way to ...
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Probability of compositions/ Dependency of standard deviation on sample size

I have following problem. Given is a 2 component solution with components A and B=1-A. I now want to know the probability of certain compositions for a given mean composition. So if the mean ...
Marc Laub's user avatar
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How to estimate shape parameter of spherical radial basis function

In this paper about positive definite kernels they introduce the extension of the radial basis function (RBF or Gaussian Kernel) $$ K_{rbf}(x,y) = e^{-\epsilon^2||x-y||^2} $$ for the unit sphere $$ K_{...
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What is the intuitive difference between covariance and the product of the standard deviations of bivariate data?

Can someone help me understand what the difference is—intuitively—between these concepts? Here's how I currently think of these things. The covariance, represented by: ... is essentially a mean area, ...
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Problem with deriving a standard deviation function

I have a function which depicts errors for a specific parameter. The function for the standard deviation of this parameter is also given, but I am having problems deriving it from the error function. ...
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Explanation for standard deviation rule-of-thumb, $s\approx \text{range}/4$

In several introductory statistics books, for a list of data $X = \{x_1,\ldots,x_n\}$, I have frequently seen the following rule-of-thumb: $$ s \approx \frac{\text{range}(X)}{4} = \frac{\max(X)-\min(X)...
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Is it possible to calculate a meaningful z-score between two values?

I have to calculate z-scores as a quality assurance test for replicate pairs of field data (water chemistry samples). I've tried processing this a handful of ways but continue to come up with $\frac{1}...
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Standard Deviation of $26$ cards without replacement

I am trying to find the Standard Deviation of $26$ cards from a normal deck of $52$ cards without replacement. I understand that to calculate it with replacement, we get variance of $1$ card as $14$ ...
quantrader23's user avatar
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Estimate standard error of population proportion based on one sample

There is a basket with unknown number of red balls ($N_r$) and green balls ($N_g$). I draw a random sample of $k$ balls without replacement and see that $P_r$ of the balls are red and $P_g$ of the ...
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Analyzing the Impact of Mean Subtraction on Series

I have two random series, $X$ and $Y$, and I've defined a third series $Z$ as: $Z = X - Y$ Now, I want to compare two other series, $Y1$ and $Y2$, to understand why $Y1$ is generally closer to $Y$ ...
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Mean and Variance Temperature Conversion

In June, New York City's daily maximum temperature has a mean of 80 °F and standard deviation of 5°F. What is the absolute difference in mean and variance in °C? I don't know what possible mistake I ...
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Linear regression for data points with given deviations?

I have a problem I fail to research properly, so I hope you may at least push me in the right direction (or maybe even provide me an answer right away?). I know how linear regression works, that it ...
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Minimizing the variance of a linear combination of random variables

Let $u, v, w, x, y$ be vectors in $\mathbb{R}^m$ where each component is an observation of a random variable $U, V, W, X, Y$. Let $\bar{u}, \bar{v}, \bar{w}, \bar{x}, \bar{y}$ be the average of $u, v, ...
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Standard Deviation of 26 Cards

What is the standard deviation for 26 cards drawn from a standard deck (each card's value ranges between 1 and 13)? Assume selection is with replacement. I saw someone approach this problem by summing ...
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How to calculate sample standard deviation of the intercepts that are obtained from all possible combinations (having $n \ge 3$ points)?

Starting with an example: Having the points $P_1(1,29),P_2(2,50),P_3(4,88)$. Then there are $4$ possible ways to choose points to find the "best" line (using ordinary least-squares). The $4$ ...
Hussain-Alqatari's user avatar
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Is it possible to scale back the average of a logarithmic number sequence to the average of the original number sequence? If so, how?

Assume you have a number sequence: 55,15,10,18,2. Then its average is 20 and the standard deviation: is 18.3. If this sequence is logarithmized its values are: 4,2.3,2.7,2.9,0.7. With a mean of 2.5 ...
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What is the standard deviation of the distribution

Suppose that you have a uniform distribution in the Interval $I_0$ where $$ I_0 \in [0,1] $$ With this as a starting interval, now you take another interval $I_1$ which is a subset of $I_0$ but is ...
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Is there a standard deviation of a continuous function?

Suppose we are given a continuous function $f \colon [a, b] \to \mathbb{R}$. The mean value of $f$ on $[a, b]$ is defined as $$ \mu = \frac{\displaystyle \int_a^b f(x) \; \mathrm{d}x}{b - a}. $$ ...
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What is the range of values after applying Standardization?

I was working on a ML model, and after applying Feature Scaling (Standardization), I observed some of the scaled value is lesser than -3 and some are greater than +3. ...
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Volatility as an Envelope for a Time Series

In time-series analysis, I keep running into graphs that look roughly like... Recalling a trig computation from an ODE book which explored the acoustic phenomena of beats, I noticed the orange ...
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