# 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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### What is the logic behind converting these units of standard deviation?

I was solving a question from high school, and it was asking for a conversion of units of one given standard deviation (σ). But I really didn't get why it is logical just converting this way without ...
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### Statistics. Calculate standard deviation and third central moment [closed]

I’m really bad at math and anything that has to do with it. Can someone help me solve this?enter image description here Click the image to see the chart and numbers. Calculate third central moment ...
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### $X \sim N(\mu, \sigma^2)$. Find $P(X > \mu +\sigma)$.

The amount of time that teachers devote to their work per week is normally distributed with an average of 60 hours and a standard deviation of 5 hours. What is the probability that a teacher selected ...
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### Why does the empirical standard deviation $\hat{\sigma}$ satisfy $E\hat{\sigma} = E\lvert X^{i}-E[X^{i}]\rvert$

Let $(X^{i})_{i=1,...,N}$ be iid random variables. Why does the empirical standard deviation $\hat{\sigma}$ satisfy $E\hat{\sigma} = E\lvert X^{i}-E[X^{i}]\rvert$? The empirical standard deviation is ...
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### Not sure about my reasoning in this exercise (standard deviation)

I was given this exercise: I did this but i am not sure if my reasoning or even my answer is okay. ...
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### GMAT related question: If the standard deviation of $a,b$ and $c$ is $d$. What is the standard deviation of $105\%$ of $a$ ,$105b/100$ and $1.05c$?

GMAT-related question: If the standard deviation of $a,b$ and $c$ is $d$. What is the standard deviation of $105\%$ of $a$ ,$105b/100$ and $1.05c$? A)$d$ b)$5d$ c)None of these d)$125\% d$ e)$1.05d$ ...
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### Recursive formula for variance with weights and decays

I have weighted observations (via importance sampling) with decay and would like to calculate (iteratively) the running variance. Both this question and this blog post focus on unweighted, non-...
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### Representative data to separate continuous data from a data in segments/bands [closed]

I am trying to have representative values to distinguish two different types of data. In the first set, the data is spread in different bands (just two in the posted example). In the second set, the ...
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### How to calculate Standard Deviation of a sample

I have 100 measurements of a device being either 0 or 1. Measurements are independent. Assuming P(0) = P(1), that is probability of getting 0 is the same as getting a 1, how would I calculate standard ...
1answer
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### Standard deviation transformations

Let R be the visual acuity readings for the right eye of a randomly selected person and L be the corresponding visual acuity readings for the left eye. It was found that the standard deviation of the ...
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### Given results of an A/B Test which variation should be preferred in tests?

It’s my first question here, so please pardon if I don’t formulate everything correct. Let’s imagine we are running an time-independent test of 2 variations that both have a probability to achieve a ...
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### what is the real Intuition behind the Standard deviation [duplicate]

A typical statistics course will define the standard deviation as "the average of the difference between the data set and the mean ". So if we tried to describe the definition mathematically ...
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### Standard deviation from sample data

Hi I am wondering how to calculate the standard deviation from sample data when you are just given the sum of $X^2$, the sum of $X$ and a value for $n$. Every formula I try gives me a error as it ends ...
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### Is scalar multiple of the t-distribution still a t-distribution?

I am modelling some prices and I am using a t-distribution. I would like to have the opportunity to change my mean parameters but keeping the same variance/volatility. So for example originally my ...
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### Finding probability of strictrly less than, when expectance and variance are given

A gardener grows cabagge. The weight of a ripe cabbage, $X$, is assumed to have normal distribution with the expectance $\mu = 2.4$ kg and standard weight $\sigma = 0.7$ If we pick a random cabagge, ...
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### Portfolio Standard Deviation equation

I'm trying to understand what this portfolio standard deviation equation means in the slide screenshot as marked. If someone could help me explain how this equation works, that would be great. When I ...
1answer
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### Help defining objective function and constraints to minimize standard deviation of list of points [duplicate]

Situation: I am trying to minimize the standard deviation between a series of points of differing heights in a list with the constraint that each point in the list can be raised anywhere from 0 to 2 ...
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### Question about confidence intervals and prediction intervals

Considering following linear multiple regression model: \begin{equation} y=X\beta + e, \end{equation} where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
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### What am I doing wrong to calculate this standard deviation?

This post mentions in passing that the standard deviation of the data set (1, 50) is about 34.65. Wolfram Alpha confirms this, saying it is $\frac{49}{\sqrt{2}}\approx 34.648$. But when I try to ...
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### Approximate overall mean and stdev of datasets with varying length

Suppose I have a list of $n$ datasets $D_i = (d_{i1},\ldots,d_{i\ell_i})$ of which I know the length $\ell_i$, the mean $\mu_i = \frac{1}{\ell_i} \sum\limits_{j=1}^{\ell_i} d_j$, the standard ...
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### What is three scaled median absolute deviation away from the median?

I am using the function isoutlier in MATLAB, where it says the following TF = isoutlier(A) returns a logical array whose elements are true when an outlier is ...
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### Normalizing and joining of independent logistic regression model's prediction

I need to train several Logistic regression models on a different set of data (with a different set of labels): ...
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