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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Annualized standard deviation from 5 annual data points [on hold]

I have 5 annual data points for a company's return vs. prior year (e.g. for year 2013, the company's return has increased by 3.4% vs. the 2012 return, etc.). I now need to calculate an annualized ...
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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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29 views

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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10 views

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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Find the Variance of X [closed]

I'm trying to find the expected value of random variable X $f(x)=\begin{cases} x, \ \ \text{if} \ \ 0 < x <1 \\ 2-x, \ \ \text{if} \ \ 1 \leq x <2 \\ 0, \ \ \text{elsewhere} \end{cases}$
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1answer
25 views

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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43 views

What's wrong with this computations?

It is true that $\int_{-\infty}^{+\infty}f(x)dx = 1$ where $f(x)$ is standard normal distribution density function $$\int_{-\infty}^{+\infty}-f(x)d(-x) = 1 \implies \int_{-\infty}^{+\infty}f(x)d(-x) ...
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21 views

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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1answer
30 views

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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1answer
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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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18 views

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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2answers
19 views

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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39 views

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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34 views

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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11 views

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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1answer
17 views

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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22 views

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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2answers
14 views

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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1answer
21 views

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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1answer
22 views

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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19 views

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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1answer
37 views

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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22 views

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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1answer
24 views

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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1answer
63 views

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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1answer
12 views

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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1answer
19 views

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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40 views

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 ...
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17 views

Standard Deviation, Percentile IQ, and Adjusting them

I've been doing a personal project to figure out how accurate online IQ tests are, so I made two of my own and had a few sample test subjects for each. For test One, I've had 21 observations (which is ...
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1answer
17 views

Uncertainty on an estimator

Well first I want to say that I have a very weak background in stats/probability but I still hope that the question I want to share with you makes sense. I have a set of binary (coming from a set of ...
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57 views

Can I calculate the new standard deviation when adding a value without knowing the original set of values?

I have these three mathematical values that describe an unknown set of values. Mean (population mean, not from sample) $\bar{x} = 3$ Standard deviation $s = 1.5$ Number of elements in population ...
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41 views

probability, normal distribution mean [closed]

Should I use a certain table for this question or should I use a special formula. A random value has a normal distribution with the mean 102.9 and the standard deviation 4.7. What are the ...
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1answer
44 views

I need help with this review question. Business Calculus/Statistics

The question is: The scores on a test have a mean of 100 and a standard deviation of 8. A personnel manager wishes to select the top 60% of applicants. Find the cutoff score. Assume the variable is ...
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1answer
14 views

Variences and adding them from independent random variables?

If I have 3 random varibles X, Y and Z and X=Y+Z then var(X)=var(Y)+var(Z), but Y=X-Z therefore var(Y)=var(X)+var(Z), it is clear that these two contridict, so what makes one of them right and the ...
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How do you calculate deviation from optimal value?

The variables I have: The optimal Tour Cost My Tour cost - I executed this 30 times, so I can get the average? Standard deviation just tells you how spread out the values are, I dont think thats the ...
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303 views

How to weight three different variables to create a ranking

I have data on the graduation rate, tuition, and average student income (a measure of accessibility) for about 7,000 colleges and universities in the U.S., and I'm trying to compose an interactive in ...
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33 views

Estimate standard deviation of sample

You have a random sample of 25 objects with mean weight of 24 grams, estimate the standard deviation of the sample. In addition, you know it's supposed to be 25 grams with a deviation of 1 gram, but ...
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32 views

Standard deviation on absolute square of complex average

I am calculating a quantity $q=|c|^2$ where I obtain $c\in\boldsymbol C$ as an average of a collection of estimates with errors: $\langle c\rangle=\sum_{j=1}^nc_j$, and the question is what error to ...
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1answer
60 views

Conclusions to be drawn from mean, median, stdev, and range

From a sample of size n = 100, the following descriptive measures were calculated: median=23, mean=20, standard deviation=5, range=35; 75 sample values are between 10 and 30; and 99 sample values are ...
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1answer
41 views

Taking the standard deviation over multiple assignments?

Lets say that a group of students all take 5 tests, with the average and standard deviations as follows: test 1: mean 43/50, SD 8 test 2: mean 23/30, SD 4 test 3: mean 56/70, SD 12 test 4: mean ...
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1answer
21 views

Probability and Standard Deviation

Hey I'm confused about how to do this kind of problem. I can't figure out how to find the standard deviation. There are on average 4 tetanus cases reported in the US each month. What is the ...
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2answers
35 views

how to find standard deviation when given a percentage?

I'm stuck on this question, can anyone help? An electronics company's biggest seller is a talking toy. Of the toys produced, 4% have a defective voicebox. A quality control tech randomly collects 250 ...
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1answer
21 views

“Reverse” distribution-tails

Chernoff, Markov and Chebyhev all give some upper bound for tail probabilities, e.g. Chebyshev gives us $Pr[|X-E[X]| \geq t] \leq \frac{Var[X]}{t^2}$. This is quite helpful, but what if I would ...
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Mean and variance: Gaussian is the most conservative assumption

"given only the mean and variance of a distribution, the most conservative assumption that can be made about the distribution is that it is a Gaussian having the given mean and variance" I've read ...
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stdev and mean from gaussian fit vs. from classical formula

I have a set of data - measured speed of molecules in water. I made a histogram and fitted it with function $$A\exp\frac{(x-B)^2}{C}$$ calculating mean and standard deviation from values B and C If I ...
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problem on standard error in sample data

From a population of 20,000 observations, a sample of 500 observations is selected. how to Calculate the standard error of sample mean if the population standard deviation equals 20.
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Problem on Standard Deviation

A man has observed the number of chocolates eaten by his son for 32 days.The total number of chocolates eaten by his son is 80 and the sum of the squares of the chocolates eaten everyday is 1000, then ...