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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Calculate percentage of a normal distribution using standard deviation

The weight of bags normally distributed with a standard deviation of $5$ $kg$. Given that $50$% of the bags weigh more than $55$ $kg$, how can we calculate the percentage of bags that weigh less than $...
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Converting mean and std deviation of degrees from Fahrenheit to Celsius

Given the conversion table of these data points of temperatures in Celsius and the respective value in Fahrenheit: \begin{array}{|c|c|c|c|} \hline C & 10 & 20 & 30 \\ \hline F & 50 &...
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Prove biased sample standard deviation [closed]

I am confused beacause it looks unbiased...someone have any thoughts for this? Show that sample standard deviation $$\hat{\sigma}=\sqrt{\frac1{n-1}\sum_{i=1}^n(x_i-\overline{x_n})^2}$$ is a biased ...
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Generate weights for mean, such that mean of weighted means is closest to $G$, while minimising std. dev. of weights

Given some fixed 'target' $T=150$, and a set of sets of arbitrary numbers $G$ in the range $0 < x \leq T\ln\left(T\right)$, for instance: $$ G=\left[ \begin{array}{ccc} p_1&p_2&p_3&...
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1-sample t-test null hypothesis p-values problem

Q-Average teacher salary in the USA is 39250 dollar. (All numbers are artificial.) Researcher randomly choosed 25 teachers from California and found that their average salary is 1900 dollar above the ...
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Compute the expected value and variance of a discrete random variable from probability table

This equation comes from Edgenuity's course of Statistics, and I am taking the course as a high school senior. I understand how to find the standard deviation. Standardized tests for certain subjects,...
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Linear Relationship for Bias Adjustment Term

I have written a post that outlines Air Bnb's adjustment for winner's curse - blog, paper. The bias term in figure 2 is said to increase linearly with delta (see blog or paper link, figure 1). However,...
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How can I cope with asymmetry when looking at forecast vs actual errors to calculate a fair measure of variation?

I have a data set that contains an actual value and two different forecasts for each datapoint. I want to compare the quality of each forecasting method. I started by drawing a histogram of relative ...
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Can you divide the error of a divided measure to get the error of each element?

as the title says, can you divide the error of a divided measure to get the error of each element? Or rather, it is statistically correct? If we have two methods of measuring weight of boxes. Each of ...
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Mean of grouped data with mean and standard error

I have a table that looks as below: The first column is the count and the second column is the mean with standard error. I would like to calculate the overall mean and standard deviation. How can I ...
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population and sample standard deviation-differences? [duplicate]

What is the statistical mathematical argument for the population standard deviation to be divided by N and the sample standard deviation to be divided by N-1? I have searched several places and they ...
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What is the cycle time for an alien signal based on signal length and distance?

If we detect a possible alien signal with the length $L$ on the frequency $F$ from the assumed distance $D$, how will the probably integral look like for the signal cycle length if we assume that the ...
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Calculating “fairness” in a Handicap Formula

I run a website dedicated to golf in which the user can configure their handicap formula with their own settings. What I would like to do is create a graph or a value rating (maybe from 0 - 100) for ...
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bounding tail probability of discrete random variable

Let $X_1,\cdots, X_{65}$ be a sequence of i.i.d. discrete random variables such that for each $i \in$ {$1,\cdots, 65$}, $\mu_{X_{i}} = 0.7$ and $\sigma_{X_i} = 0.1$. Then, with $Y=X_1+\cdots+X_{65}$, ...
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Standard Deviation for a Known Subgroup

This is the first time I've looked at Standard Deviation for about 25 years and I would really like to get this right, but I'm failing at Google (helpful though it's been!). My query is around what to ...
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Significance Hypothesis Testing

Given an assumed mean of 60, a standard deviation of 6, and a population with a sample size of 50 and a population mean of 62.6, I was able to set up two hypotheses, H0, $\mu=60$ H1, $\mu \ne 60$ I ...
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Distribution and Standard deviation

Let $X$ be normally distributed with a mean of $105$ and standard deviation of $10$. What is the probability that $X > 112$? What value of $X$ does only the top $5\%$ exceed ?
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How do I calculate this sampling error?

If I sample individual integer values $0$ to $100$ from a distribution $100000$ times and record the counts for all integer values between $0$ and $100$, how do I calculate the $95$% error bars for ...
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Deriving formula for variance

I am trying to derive the simplified variance formula and am abit stuck on a part of the proof: $$ \hspace{-7em} \sum_{i=0}^n (x_i-\mu)^2 f(x_i) = \sum_{i=0}^n x_i^2 f(x_i) - \mu^2 $$ $$ = \sum_{i=0}^...
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Redefining objective function to incorporate x-axis

I recently asked a question about minimizing the standard deviation from a list of equidistant values and I received a great answer here: https://math.stackexchange.com/a/4089367/907708 However, now I ...
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Standard deviation of a Random Variable (with respect to 3 other random variables)

I have the following problem Assume that you have three independent Random Variables X1, X2 and X3. The expected value for each Random Variable is ...
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Repeating an event until the actual mean equals the expected value (within a suitable degree of accuracy). How many times?

If I had a spinner, where each probability and value is known, how many times would I have to spin it to say that there is a 99% chance that my accumulated winnings' mean is within $0.01 of 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 ...
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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 ...
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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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Calculating algebraically the variance of finite series

Let me motivate my question with an example. Suppose I have two finite series $A$ and $B$. Series $A$ has the following values: $-1/150, -1/149, ... , -1/141$. Series $B$ has the following values: $-1/...
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Compute Variance of a the ratio of different terms : which term to consider as random variable?

I have the following expression with random variable $X$ : $X = \bigg(\dfrac{b_1^2}{b_2^2} + \dfrac{N(\ell)}{f(\ell)}\bigg)$ with $b_1$ and $b_2$ constants and $\ell$ a variable. Can I write : $\...
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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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Sample Variance and Population Variance for Ungrouped data

A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained: Smokers: $69.3, 56.0, 22.1, 47.6, ...
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Standard Normal Distribution Question related to Finance

Percentage daily returns on a financial asset is modelled through a normal random variable. You want to classify returns that differ from the mean by more than $3.4$ standard deviation as "...
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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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When is the standard deviation of the squares of a random number greater than the square of the standard deviation of those numbers?

I was playing around with the uncertainty of the kinetic energy operator in quantum mechanics, and really desired to have the following inequality be true: $$\Delta K=\frac{1}{2m}\Delta (p^2)\geq\frac{...
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Is there none numeric way to find the value of $x$?

Lets say I have the givens $$x=1, \quad y=75.0635 \pm4.10915$$ $$x=2,\quad y=80.2912 \pm 7.76671$$ $$x=3, \quad y=98.2725 \pm 5.76051$$ $$x=4, \quad y=125.963 \pm 7.15494$$ $$x=5, \quad y=125.728 \pm ...

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