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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Standard Deviation for Normally Distributed Bell Curve - Worded Problem

My working out: Z = (14-9.5)/2.25 = 2 % less than 2 = 95% Answer is 97.5 % .... no idea...
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Is Standard Deviation the same as Entropy?

We know that standard deviation (SD) represents the level of dispersion of a distribution. Thus a distribution with only one value (e.g., 1,1,1,1) has SD equals to zero. Similarly, such a distribution ...
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Summing up Standard Deviations - best approximation

For a long data series the overall Standard Deviation shall be collected. However, due to memory constraints the data has to be aggregated per day - in a way that only one number is stored per day ...
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149 views

Given Standard Deviation and Population size, how can I calculate the number of population at mean

As per the title, I'd like to calculate the number of the population at mean, given a std.dev and population size. The use case for this, is Mobile Phone push notifications. I send the notification ...
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36 views

How to answer probability question with basic std dev statistics

I have a data sample, say: $69$, $72$, $100$, $87$, $57$, $123$, $110$. Knowing the standard deviation and the mean what is the answer to the question: What is the number ($x$) for which $n\%$ out ...
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Question about an article by Nassim Nicholas Taleb about the problems with standard deviation.

The article by Nassim Nicholas Taleb says that using standard deviation is flawed and is poorly understood and mean absolute deviation should be used. Because this article is short, and I don't ...
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41 views

Standard deviation: When to use which sum-coefficient?

I'm wondering when to use $\sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ and when to use $\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ which I have both seen in ...
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177 views

How is the Standard Error and the Unbiased Estimate of the Variance Related?

I am going through a statistics textbook and there are two similar formula's that I cannot seem to grasp, one under the "Sampling Error" section and the other under the "Unbiased Estimator" section. ...
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Find the variance of $x$ when the standard deviation is given in the form of $ax+b$.

The standard deviation of $3x+7$ is $4$; then what is the variance of $x$? I know that variance is the square of the standard deviation but how does $3x+7$ and $x$ relate?
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Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
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119 views

can STD of subsets be used to arrive at the STD of the whole set

Assuming I have a set of values called S and the STD of S is Xs. Let's say I split S into two subsets S1 and S2 with standard deviations X1 and X2. The number of elements in S1 and S2 are called W1 ...
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The rule of the 3 sigmas -— how many times multiply the sigma to get 85%?

$\sigma c=\sqrt{\overline{R}(\sigma S)^{2}+\overline{S^{2}}(\sigma R^{2})}$ where, $\sigma c$ --- the buffer stock --- needed for maintaining the risk of stockouts, is used by logistitians ...
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41 views

Confidence interval and normal distribution

For question (a), is the answer 0.7143? For question (b), is the answer 10.85 and 11.95 ?
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48 views

I need a probability statement

I need some help with this question please. Make a probability statement about a group of workers who produced product data with a mean of 20 and a standard deviation of 1.03.
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58 views

Standard Deviation: Can I remove some data?

Suppose That I have measured property "X" in 16 points of a rigid body. This rigid body is consisted of two different materials. In one of them, property X is around 1, and in the other X is around 5. ...
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910 views

Normalizing data to a given value.

I would like compare the data by normalizing it to a given value. for example: [20,30,40,50,60,70] How do I normalize the given set of elements to its first value, ...
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35 views

mean and standard deviation of students taking a test

6 percent of all students of a class will not pass a test. There are 450 students taking this test. Let X represent the number, out of 450 students, who will pass this test. Find the mean and standard ...
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41 views

Solving Probability using standard Deviation and Mean

Given a normal random variable with mean 90 and a standard deviation 3, find the probability that x is greater than or equal to 86.67 and less than or equal to 96.33
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Exclude an RGB color from a set

I'm currently implementing an algorithm to split an image into smaller chunks, based on straight line separators. Here's the image I'm processing. It's very small, so you may want to save it and ...
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59 views

Calculation the Standard Deviation

I want to calculate the standard deviation of the following numbers: 30, 45, 45, 60, 75, 80, 90, 100, 110, 120. As far as I know, that would be ...
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126 views

Finding the variance of a normally-distributed random variable

X is a normally-distributed random variable, and $P[X<20] = 1/10 = P[X>100]$ I am trying to solve for the mean and the variance. I know that $\mu=60$ by symmetry. How can I solve for ...
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41 views

Convert list of test results into a comparative score

My students have completed a touch typing test that have given them a WPM (words per minute) result. I now want to give a score to those results out of an arbitrary number, say 10. I will later use ...
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Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
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Probability for Rolling 10 tethedrons 100 times

I am pretty confused about how to form the probability distribution function of the following question: Suppose you have a tetrahedron with numbers 1,2,3,4 on respective faces. If you roll 10 such ...
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Relation between standard deviation and mean in random processes

In a Poisson distribution the square of the standard deviation $\sigma$ is equal to mean $\mu$ ($\sigma^2=\mu$) and in a binomial distribution $\sigma ^2=\mu\,(1-p)$ (with $p$ the probability of ...
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Central Limit Theorem: asymptotic distribution

I keep reading in the documents about the asymptotic distribution of the CLT. I am learning things by myself so try to figure it out on my own and don't have a teacher to ask the question to. So it's ...
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376 views

Stuck…please help to understand how formula works in order to Find the standard deviation in normal distributions

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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statistcs z-table standard deviation question…Please help.

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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52 views

Please help ! A bit confused…I need to figure out exactlty what the question is asking me to determine.

Suppose that over a certain period prices of stocks in the S&P 500 can be approximately modeled using the normal distribution with $\mu = \$40.35$ and a standard deviation of $\$8.97$. The data ...
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standard deviation calculation using covariance?

i require a formula to calculate the standard deviation using variances of three or more variables (lets call them a,b,c) and the covariances between them. To complicate matters more i only need a ...
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Finding Missing Observed Scores given standard deviation and mean

The question that i'm being asked it: the mean of 10 observed scores was 20 and the standard deviation if 6.0. the observed scores are {16,11,20,24,29,24,16,20,,} what are the two missing scores I ...
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233 views

confidence interval of binomial disribution using standard deviation

Just as the normal distribution has the 68–95–99.7 rule with 68% of the data within +- 1 standard deviation and so on, does the binomial distribution too has something like that. Or does its being a ...
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Relationship between expected and actual value [closed]

Consider a zoo with two animals: an elephant and a lion. The elephant's expected lifespan is $70$ years, but it lives to be $65$ years ($SD = 7$). Likewise, the lion's expected lifespan is $22$ years, ...
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standard deviation of binned sample

I have to calculate the rms size of some sample (let's say 1D for this case). When I only have limted resolution my rms value gets bigger. What's the name of this effect again? Is there a way to ...
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37 views

Probability question help

A company that sells annuities must base the annual payout on the distribution of the length of life of the participants in the plan. Suppose the distribution of male participants' lifetimes is ...
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163 views

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need? I may not be using the correct terminology so here's a graph: Based on this, if you ...
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Standard deviation of less than one

How would I find the approximate percentage of values within a standard deviation of less than one on the normal model? Chebyshev's rule is only used when the standard deviation is greater than or ...
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Estimate the true mean: given only measurements above a known threshold

I have a computer-generated logfile which shows events which took longer than a particular time threshold (say 1 second for the sake of argument): if I measure the mean of these measurements, it seems ...
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How do you determine the sample size of a normal distribution?

I am presented with the question: The photoresist thickness in semiconductor manufacturing has a mean of 10 micrometers and a standard deviation of 1 micrometer. Assume that the thickness is ...
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Calculate risk that occurs p% of a time

In a search of a way to calculate variance for risk management I found the following formula (n1, n2, n3 are data points): ...
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Expected Value and Standard Deviation for sample

Randomly selecting 50 people from a population, 45% say 'YES' and 55% say 'NO'. Assuming that the true percentage of people in the population who say 'YES' is 48%, what is the expected value and ...
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Equivalent standard error for different populations

So I have population A and population B. The demographics are similar (assumes that the true expected value is the same in both populations). Population B, however, is twice the size of population A, ...
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970 views

Converting standard deviation number

This is math finance question. I'm trying to figure out the formula for converting the standard deviation of % changes in prices for a sample of days into the standard deviation of % changes in prices ...
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Normal distribution probability problem.

There are lots of salmon in a pond and their length (in centimeters) obeys normal distribution $N(70, 5.4^2)$. You and your friend go fishing and decide to continue fishing until both of you catch at ...
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Calculating the expected value and the standard deviation of the total profit.

Company sells 2 kind of cars, Lamborghinis and Ferraris, and the sales of the cars are independent. From every sold Lamborghini the company gets 10000 dollar profit and for every Ferrari the company ...
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Standard deviation: mathematical manipulation

I am learning about standard deviation. In the book I am reading it defines standard deviation as: $$\sigma^2 = E[(x - E[x])^2]$$ so far no problem. In then states "simple mathematical manipulation ...
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22 views

Interquartile Rang concept / Problem?

If a set of data consists of only the first ten positive mulitple of $5$, what is the interquartile range of the set ? I have tried to solve but my answer is wrong..
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Understanding weighted standard deviation

Here is the formula that I use for weighted standard deviation: http://www.itl.nist.gov/div898/software/dataplot/refman2/ch2/weightsd.pdf. My question is: why do we care about the number of nonzero ...
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Finding 'symmetrical range' from mean.

A machine used to make butter where its masses are normally distributed with mean m and standard deviation s.It is found that 5% from these butters are having mass more than 85g where else 10% are of ...
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Length of Gaussian distributed variables

Suppose I have a set of random variables $x_1,...,x_n$ s.t. $x_i\sim N(\bar{x}_i,\sigma_i^2)$. And I define a new variable $x=\sqrt{x_1^2+...+x_n^2}$, then will $x$ also be normally distributed? And ...