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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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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861 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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665 views

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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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 ...
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How do I determine a standard deviation with the mean and range known?

How do I determine a Standard deviation with the mean and range known?
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Explanation for correlation coefficients and standard deviation rolling 3 dice

Roll in MATLAB 500 times threesome-dice (3 dice) and sum them.Find in addition: max and min in each sequence mean values of sum/min/max. deviations of sum/min/max. correlation ...
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Propagation of standard deviation for random variable with Markov Property

I have a discrete random variable, $X \in \{0,1,2,3\}$. Define the indicator function: $$ 1_{k}\left(x\right) = \begin{cases} 1, & \text{if $x=k$} \\ 0, & \text{otherwise} \\ \end{cases}$$ ...
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Need help with derivation of conditional expectation

The following is taken from the book "Mathematical Statistics for Economics and Business": \begin{align*} E\left.\left( \left[ Y-h(x) \right]^2\ \right\vert\ x\right) =& E\left.\left( ...
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333 views

Compare standard deviation with out using the standard formula

I very well know that Standard Deviation is the measure of spread of the data. If the data has higher deviation from its means then it has higher standard deviation. What if the data has same mean ...
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467 views

Removing outliers with standard deviation - is it possible to end up with an empty dataset?

There is a fairly standard technique of removing outliers from a sample by using standard deviation. Specifically, the technique is - remove from the sample dataset any points that lie 1(or 2, or 3) ...
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137 views

Why calculating variance this way is wrong?

I'm conducting a set of computer simulations (of membrane). I sample a property (area, $a$) in the following manner: $ A = \sum _1^N a \\ S = \sum _1^N a^2 $ During my data analysis, I calculate ...
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115 views

Mean or standard deviation?

Which one of mean or standard deviation can used to solve the following problem? A light bulb is considered defective if it lasts less than 400 hours. The following claim is made: 'Brand A ...
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190 views

Find the standard deviation of $ \frac{\gamma}{\sqrt{2\pi\sigma}}\exp\left(-\frac{\gamma^2}{\sigma}\frac{(x-\mu)^2}{2}\right)$

Given $\frac{\gamma}{\sqrt{2\pi\sigma}}\exp\left(-\frac{\gamma^2}{\sigma}\frac{(x-\mu)^2}{2}\right)$ as a normal distribution PDF with mean $\mu$, I'd like to solve for the std deviation in terms ...
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Is population standard deviation useful in the computers era?

Sample standard deviation used to approximate the population standard deviation. I can imagine this was very handy when you were dealing with a large population in pre-computer era. Now thanks to ...
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Trying to understand the standard deviation's formula [duplicate]

I have just started learning standard deviation and I'm trying to understand the formula. $$ s = \sqrt{ \frac{\sum(x-\bar x)^2}{n-1} } $$ Can anyone explain to me the square (and square root) part? ...
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968 views

Composite Standard Deviations

Normally, in AP Stats we were taught that to find the standard deviation of a new set of data, for example: to compute $stdv(A - B)$, you say $$stdv(A - B) = \sqrt{\text{var}(A) + \text{var}(B)}$$ ...
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Data estimation based on progression

Given a data-set $x$ and $y$. x | y ------------------ 153,000 | 0.058848 332,641 | 0.36352 506,629 | 0.53 If $x$ being the number of database records ...
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Regression vs. Normal Distribution

I have to estimate something using historical data. Should I find the equation of the curve of best fit to estimate? Or use a confidence interval, standard deviation, and a z-score to calculate it? ...
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Estimating time

I have some data about a number of projects that have been categorized. For each project, I have the proportion of the total project length that was spent on testing. For each category, I have to ...
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Hypergeometric Distribution Probability (mean, variance, Std Deviation)

The distribution of the number of children per household for households receiving aid to dependent children (ADC) in a large eastern city is as follows: 5% of ADC households have one child, 35% of ADC ...
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Means and standard deviations.

Given three independent random variables $X_k$, the means and standard deviations respectively are $X_1 = (A, X)$, $X_2 = (B, Y)$, $X_3 = (C,Z)$. (1)What is the mean of their sum? (2)What is the ...
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Calculate the new average using standard deviation?

This is for a programming exercise. I have: the last average value the last standard deviation the total number of values I need to be able to add a new value to my average without knowing the ...
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Central limit theorem - std dev away from mean

I was reading about the CLT and found something that I think people use interchangeably. On one hand I found that 68% of the means are 1 standard deviations from away and 95% are 2 std dev. On the ...
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standard deviation of a certain distribution

If I have a list of N outcomes of drawing a number from the set {-1\$,+1\$}, and I know that the probability of getting (in a single draw) (-1\$) is p, and probability of getting (in a single draw) ...
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Quadratic and geometric average

I'd like to find the find the quadratic average and the geometric average. To do this I have these informations : The standart deviation, the arithmetic average and the number of values. I know the ...
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572 views

Merging standard deviation of two groups with duplicates

I am using Parallel Algorithm (http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm) to merge standard deviation of two groups Can we merge two groups if there are ...
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How can I mathematically show the similarity between these 3 plots?

I have 3 3D plots of field strength measured around an antenna. I want to calculate the mathematical similarity between the points of the field patterns. How can I do this? thanks
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Can a Covariance matrix have negative elements?

I have a $N \times N$ covariance matrix $C$ of a multivariate Normal distribution. Can any of the elements of the Covariance matrix $C$ be negative for a real-valued distributions ?
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Recursive formula for variance

I'd like to know how I can recursively (edit: iteratively) compute variance, so that I may calculate the standard deviation of a very large dataset in javascript. The input is a sorted array of ...
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Standard error and p-values

I am a scientist who is currently doing a BSc. I did some stats a few years ago but since haven't touched it. I'm not sure how to calculate p-values for my data. A bit of background is that I am ...
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250 views

Finding a percentile in Excel

I am writing a program using excel and I need to find the percentage of a number. I have a few sample numbers and their percentages. 2.3% - 5.013368 5.0% - 5.238858 10.0% - 5.480078 25.0% - ...
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variance reduction

Say i have $n$ variables with variances $V_1,V_2,...V_n$. The sum of the variables will have a variance of $V=V_1+V_2+..V_n$ .Now if i am given N total simulations to reduce the variance V, how do i ...
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Probability of being within one standard deviation of mean given only a moment generating function

I am trying to figure out how to approach this: For starters, I calculated M'(0) and M"(0), which allowed me to find the mean and variance. I got 2 for the mean and 1.6 for the variance. But now, ...
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Variance of a sum of correlated variables.

http://www.maths.qmul.ac.uk/~ob/MTH6121/moddocs/chap1_4.pdf I'm currently reading over some notes, linked above, and I've come across a difficulty with proposition 1.27(page 12). Underneath, it says ...
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Standard deviation formula

I'm having a lot of doubt on the formula of the standard deviation (in linear regression). My teacher and my syllabus say it's (for $\sigma_x$): $$ \sigma_x = \sqrt{\dfrac{\displaystyle\sum ...
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Statistics Question: Fixed revenue, variable costs

Given a distribution of costs per customer, with a fixed revenue per customer, how would I work out what the profit would be on: mean cost: $\$3.00$ standard deviation cost: $\$2.00$ revenue: ...
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Is there a better measure of variation for fractional numbers than standard deviation?

For a task I need to do, I'm finding the variance / standard deviation of a set of numbers that are between 0 and 1. When I square the difference from the mean, the square will make the difference ...
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Find standard deviation given standard deviation

How would I find the standard deviation of a value, V that is the average of other values, say heights of people, given that I have the standard deviation of the heights? I'm looking to improve my ...
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Calculating the standard deviation of the sum of a series of randomly distributed variables

Say I roll a six-sided dice 100,000 times. I know that the resulting sums will be normally distributed around a mean of 3.5 How would one go about calculating the standard deviation of the ...
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If three groups of unequal sizes have the same standard deviation but different means, will the SD of the pooled data be the same?

Will the standard deviation of all data in three unequally-sized groups each with different means be the same if each group has the same standard deviation? For example, I have a data set as follows: ...
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7.7 standard deviations away from the mean?

I'm confused. I have a problem where I have to find the probability that x is below the z value 7.7. My z table only goes to z values of 3.4. How do I calculate this? These are the hints my teacher ...
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Standard deviation of the weighted mean [duplicate]

How do you find the standard deviation of the weighted mean? The weighted mean is defined: $\bar{x}_w = \frac{\sum{wx}}{\sum{w}}$ The weighted standard deviation (since it is not specified, I take ...
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How to calculate standard deviation and use three-sigma rule for couple variables?

Generally, I have the following data: CampaingOne 49% CampaingTwo 41% I need to use the three-sigma rule and check if the second value is in the interval [- 2 ...
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How does standard deviation depend on data?

I've got a problem: I take a random variable, assign values to it and than I have to invent two different probability distribution functions with similar mean values (+-5%), but in the second function ...