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.

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Normal distribution of juice

Quantity of juice in a pack of 1L is normaly distributed with average (mean) 950ml, and with standard deviation of 10ml. What is the probability that random pack of juice contains less then 945ml of ...
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Finding probability given mean and standard deviation

I don't know how to approach this problem: X is normally distributed with a mean of 200 and a standard deviation of 10. Find P(X ≥ 203)
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Finding groups with minimum mean deviation

Is there any algorithm that groups consecutive elements in an array that gives the minimum mean deviation. For example we are given an array a=[1,2,3,4,8,2,3,5] There can be many "consecutive" ...
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Beginner Econometrics question about probabilities for a normal variable

$Y \sim N(\mu, \sigma^2)\implies (Y-\mu)/\sigma$ Prove that this has a Mean of $0$ and a Variance of $1$.
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When plotting a bell curve from an array of values, is it possible that +/- 2 standard deviations from the mean can fall outside the range of values?

First, this is not homework, it is actually for work. It's been a couple of years since I've done stats and need some help! I've googled for this problem but was unavailable to find any resources that ...
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44 views

Finding the 99% of a normally distributed graph

The heights of adults are normally distributed with a mean of 187.5 cm and a standard deviation of 9.5 cm. A standard doorway is designed so that 99% of adults have a space of at least 17 cm over ...
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280 views

Statistics - Calculating Mean given standard deviation and percentage.

This is one of our homework problems for Statistics. I'm really stuck on this one, and it would be great if someone could show me how to solve this, or at least set up the equation. The weights of ...
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How can I describe uniformity in a group of values?

I have a matrix of 128x128 (6384 numerical values) referring to light intensity. I will like to know how to calculate the uniformity of the values and I am currently using the standard deviation to ...
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33 views

Unbiased sample standard deviation of a custom/unknown probability distribution

Hi i must determine the unbiased sample standard deviation of an unknown probability distribution.I dont have the data of the full population so i must work with a sample. Now according to Wikipedia ...
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Random variable variance

I have the model yi=β1+β2Xi+ui where ui∼iid N(0,σ2). I estimate β1 and β2 by drawing a straight line between the first (x1,y1) and last dot (xn,yn). So, β̂ 2 will be the slope of this straight line. ...
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How to estimate the standard deviation in this normal distribution?

There is this simple looking basic statistics question that asks to estimate its mean and standard deviation. I have some doubts and just want to make sure whether my working is correct. For part ...
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Standard deviation in normal distribution

A manufacturer uses a machine to make metal rods.The diameter of the rods follow a normal distribution with a mean of 1cm and a standard deviation of 0.02cm If the standard deviation of the diameters ...
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Finding the percentile of a value given other percentiles

I am using someone else's research and only have part of the data. I want to find the percentile of a value, such as 350.2, based upon the data given. The following is known: mean = 308.2 The ...
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Showing deviation of data on a fixed scale

I'm creating a chart in D3 which shows the Mode from a large (1mil +) dataset; and colors it according to the standard deviation of the dataset. But the issue is that I need to map the range (Red ...
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Standard deviation of travel times

Suppose that travel times for Swinburne students are normally distributed with mean of $32.5$ minutes and a standard deviation of $5$ minutes. Complete the following sentence, giving figures correct ...
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135 views

Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...
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32 views

GRE - Standard Deviation

The frequency distributions shown above represent two groups of data. Each of the data values is a multiple of 10. Quantity A = The standard deviation of distribution A Quantity B = The standard ...
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Weighted probabilities assigned to a two stock portfolio

Does anyone know how to input a two variable portfolio with uneven weighted probabilties into an HP10bii+? By uneven I mean the weightings are not in increments of 10% and thus you can't simply equate ...
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Gaussian of different standard deviation and sample spacing

For given a set of samples position (e.g. $-2,-1,0,1,2$) I can define the correspondent, normalized, gaussian weights for a gaussian with std. deviation $1.0$. I know that if I scale all the sample ...
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combined standard deviation

I am new to Standard Deviation. I have taken a 2 small samples of Data and obtained the mean, and Standard Deviation. I have copied and pasted a picture of my spreadsheet. As you can see i have ...
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56 views

Average and Standard Deviation for Angular Values

I'm trying to characterize an inexpensive accelerometer that provides (roll, pitch, yaw) values by generating basic running statistics (mean and standard deviation). But I'm unfamiliar with ...
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Variance reduction factor using gaussian filtering

I am currently trying to find the variance reduction ratio using gaussian filtering. For a simpler filter (as mean filtering for example), I am able to calculate it easily to find the well known ...
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Normal Distribution,standard deviation and probability question.

According a study, the duration of a match in World Cup is approximate normally distributed with the mean 111 minutes and standard deviation 5 minutes (including the break between the halves). ...
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Does “Expected Absolute Deviation” or “Expected Absolute Deviation Range” exist in stats and have another name?

So everyone is familiar with Variance and Standard Deviation from high school, but it seems no one has any familiarity with a philosophical justification for such weird, seemingly arbitrary measures. ...
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finding the variance of a complex scenario

construct a sequence of cubes with one vertex at the origin and having lengths 1/2^x, x=1,2,3,... Select a point randomly from the unit cube with one vertex at the origin and sides of length 1. Let ...
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Determine standard deviation of nonlinear model parameter?

I have some experimental data to which I fit $h+e^{-\gamma t}(a\sin\omega t - \phi)$. The result looks like this: My ultimate goal is to find $h$ values. Now, I could find something similar to $h$ ...
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Summing standard deviations? or summing variances?

I have a method for making measurements. Within this method there are four separate variables that can influence the measurement (i.e. variation). I have individually tested each variable (by making ...
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How to derive a Gaussian mean's functional dependence on a variable

I have three variables: $E, I,$ and $X$. $I$ is a function of $E$: $I(E)=gauss(\mu(X), \sigma=1)$ I sampled this distribution with a very simple $\mu(x): 3\times x$. I want to fit that data to ...
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How to add standard deviation regarding MATLAB function normrnd(mu,sigma)?

My question depend on this scenario which is as follows, I used a MATLAB function "normrnd(mu,sigma)" with mean 'mu = 0' and S.D 'sigma = 5', to generate a normal random number "R1". I added this ...
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How to calculate Standard deviation with mean 0 and Min and max value on x-axis is -1 and 1 respectively?

How to calculate Standard deviation with mean 0 and Min and max value on x-axis is -1 and 1 respectively? It is of-course a normalize distribution. I apologize in advance for stupid question.
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Adding stochastic variables random variables where one has time component

Based on GLS regression I have identified two random variables lets call them A & B ...
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Population confidence interval from sample SD and sample mean?

A sample has: $$\text{a sample size } n = 70,$$ $$\text{sample standard deviation } s = 184.43,$$ $$\text{and a sample mean } \bar{x} = 564.15.$$ Compute a 95% confidence interval for the population ...
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Is the variation of the mean 0, and the variance of standard deviation just the variance?

Just trying to get some properties straight. Was looking at a problem online which reads: Let X be a random variable with mean μ and variance σ2. What is the variance of X/σ+10μ? The solution of ...
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Monte Carlo standard deviation of the mean estimate too small.

I'm doing a Monte Carlo calculation and use the standard deviation of the mean $\sigma_M$ as the error. To get an estimate of this from the regular standard deviation I use $$\sigma_M=\dfrac\sigma ...
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Confused on Expected Value

I have this question in which I have solved so many times but unsure of the answer i have. could anyone help out? ** A cpu manufacturer has a machine which produces microchips. The probability ...
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Variance test: how to tell which is sample 1 and sample 2?

I'm using this variance test to see if I have unequal variance in my data: I am not told which is sample 1 and sample 2 in the questions, just the alternative hypothesis. So is there anyway I can ...
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Clarification on z-score

I have been reading a Statistics book and they show the following formula for z-score: $ z = \frac{x - \mu}{\sigma}$ And then they explain about the $\mu$ and the $\sigma$ in the formula like this: ...
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Estimating “task duration” variance through questions in a questionnaire

I am working to estimate the average task duration for complex processes - a total of 19 tasks / processes (each task made of several subtasks of varying duration). I will be organising a ...
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Find StdDev of a percentage list

I need to find Standard Deviation of a percentage list, e.g. [0.5, 0.8, 0.8] in Python would give: ...
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SD from Mean and Median

Given the mean and median of a dataset, is it possible to compute the standard deviation of the dataset?
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Value of n to ensure the mean is within a 95% confidence interval

A random sample of size n is obtained from normal distribution. Calculate how large n must be to ensure that the sample mean lies within 0.25s.d of the mean with probability of 95%. I know the ...
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Bioststistics review

The Mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2mg/dl. If the mean and standard deviation of serum creatinine in the ...
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Standard deviation with multiple means and deviations

The amounts of a certain mineral that can be produced in a day from mines $1$, $2$, and $3$ are independent normal random variables with means equal to $80$, $90$, and $75$ pounds, respectively, ...
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What are different ways to compute the significance of an A/B test?

It seems that many people use sample mean/ std deviation or std error which is sqrt ( p * (1-p)/n ) but this assumes that the underlying distribution is binomial.
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Exponential deviation with two $x$ values

I recently got interested in this topic of standard deviation. My TA did not have any time to go over this topic so I was trying to teach myself it recently. My TA said if he had more time he would ...
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Clarification: Expression to calculate the standard deviation when data is scaled to interval [0,1]?

For an experiment, the standard deviation (SD) is entered as a parameter for generating gaussian noise. The SD value is mentioned to be 25 when data (a matrix) has integer values in [0,255]. If the ...
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Margin of error for quotient of two measurements

I need to find the total margin of error for calculating velocity, while I have margins of error for time and distance. Actually the margins are the same (as both measurements were based on GPS - but ...
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finding percentiles with standard deviation

This is a question on my worksheet that I'm not sure how to start: If you know that the mean salary for your profession is $\$45000$ with a standard deviation of $\$2000$, to what percentile does ...
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Standard deviation shouldn't reduce?

I need to do a algorithm to calculate an integral via Monte Carlo Method, and for a purpose of simulation, I need to calculate the standard deviation of a sample generated in my program. My problem is ...
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A Sample with two Standard Deviation

Question : In a batch chemical process, two catalysts are being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1 and a ...