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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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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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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269 views

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 ...
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What is the purpose of subtracting the mean from data when standardizing?

What is the purpose of subtracting the mean from data when standardizing? and What is the purpose of dividing by the standard deviation?
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finding n value basic statistics

I have some practice homework questions. I did the first one I will go over the steps please tell me If I am doing it right. a) As mentioned earlier, it is claimed that 70% of households in Ontario ...
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How to calculate standard deviation for a series containing both positive and negative numbers?

I got a stream of numbers in one of my apps to represent an electrical signal. I've observed that the signal ranges from -100 to +100. Other than that, the signal is fairly random and crosses 0 in ...
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Finding the standard deviation of a set of angles.

My question is given a set of angles in the form of degrees minutes and seconds once finding the mean how do you find the standard deviation. I know how to find the average or mean of a set (see ...
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How to vary increase of x as n increments through the Fibonacci series?

Excuse my incorrect use of terminology, I hope my question is clear: I am coding a Python module which tests whether a given number is a member of the Fibonacci series. No problem with that. ...
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Compare Standard Deviation

The Obama vacations have cost an average of 4 million and a standard deviation of 5 million. The Bush vacations have cost an average of 3 million and a standard deviation of 2 million. What is more ...
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Standard Deviation and Variance

Since the start of the Obama presidency, the average number of minutes playing golf each week is 160 minutes and the standard deviation is 20 minutes. The average number of minutes attending cabinet ...
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Weighted Standard Deviation for Histogram Bin Height

I'm plotting some binned data in the form of a histogram. Say I have 10 data points, each composed of a bin to be placed in, and then a "height". Then I might have something like: Bin Height 0 - ...
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Statistics Question: Revenue & Cost

Data for costs of production for a firm every month from January 2001 to December 2002. Data is denoted by $d_1, d_2,...,d_{24}$. The following info is calculated from the data set. Mean cost = ...
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Uniform distribution, Expected value and standard deviation for proportion of observations in a subintervall

$X\sim U(0,1)$. Divide the interval [0,1] into k equal subintervals. Then $X_1$=the number of observtions on the first interval. Define the new variable $Y_1=X_1/n$, where n is the number of ...
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Simple standard deviation question using stocks as example

The following table is from page 171 of Fundamentals of Investing (11th edition) by Gitman, Joehnk, Smart. Please consider only the X, Y and XY columns (second, third, fifth). Portfolio XY comprises ...
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Distribution of proportions of each row cell

I'm trying to make sense of some data I have. Below is a simplified version of how data is structured. To get some context, the table shows the distribution of an investor's investments across ...
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Advantage of Relative Standard Deviation (RSD)

The definition of RSD is given below: Relative Standard Deviation: In probability theory and statistics, the relative standard deviation (RSD or %RSD) is the absolute value of the coefficient ...
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How to average numbers with high standard deviation

I have a set of n numbers that I need to review and come up with the closet average. The set of numbers may or may not have a high standard deviation. Below is an example... Set of numbers.. ...
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What is the probability that the 2002 mean salary of a random sample of 50 baseball players was within $20,000 of the population mean, μ .

Let μ be the mean annual salary of Major League Baseball players for 2002. Assume that the standard deviation of the salaries of these players is $107,000. What is the probability that the 2002 mean ...
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Calculating $P(X-E(X)\geq \mathrm{SD})$ for a normal random variable $X$

If you'd have to calculate the following probability of an $X\sim \mathrm{Normal}$: $$P(X-E(X)\geq \mathrm{SD}),$$ how would you calculate it? And if the calculation will be for $4\cdot\mathrm{SD}$, ...
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What is difference between standard deviation and Z-score?

I have read several explanations of standard deviation and z-score, I know how to it calculate them but I am not sure what is differences betwen them. Can someone explain it to me? When is suitable ...
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Percentile for a Given Z-Score

Disclaimer: Statistical math person I am not... I'm a programmer that has been tasked with finding the percentile a child will fall in depending on their weight and age according to the CDC. The ...
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Normal Distribution from Standard Deviation?

So I have a data set $(x_{1},y_{1}), (x_{2},y_{2}),\dots,(x_{n},y_{n})$ and from it I have the values of $\sum x$, $\sum x^{2}$, $\sum y$, $\sum y^{2}$, $\sum xy$. My question is, how do I find a ...
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How to determine if Standard Deviation is high/low

I have derived the following response time data for a performance test I am running: Min - 8sec Max - 284sec Average - 28sec Standard Deviation - 27sec What does the standard deviation say about the ...
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Probability of randomness from a given z-score

From a given z-score, what is the formula for calculating the probability of the deviation being due to chance? e.g. Given z = 1.2 standard deviations The chance probability p = 0.11507 How did we ...
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Statistics, calculating mean and standard deviation

IF the mean of a set of scores is 80 and standard deviation is 10, explain the effect on mean and standard deviation in case following changes are made to each of the scores 1) adding 5 2) ...
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Bounding the standard deviation of a bounded random variable

Suppose $X$ is a random variable (discrete or continuous) whose values lie in the segment $[0,1]$. Is it safe to say that the standard deviation of $X$ is between $0$ and $\frac{1}{2}$?
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How to assure quality control to a 4% level of significance based on a 200 item sample with 24 defects?

For quality control purposes we have to accept or reject a large shipment of items. In order to do so we collect a sample of 200 items, 24 of which are defective. The manufacturer claims that at most ...
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Hypothesis testing for Variance - choosing a null hypothesis.

A gun-like apparatus has recently been designed to replace needles in administering vaccines. The apparatus can be set to inject different amounts of the serum, but because of random ...
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Is it possible to calculate the mean and standard deviation from a median and quartiles?

Any advice would helpful. I understand that the reporting of median and quartiles for small samples is an indication of skewed data. If such is correct, then is it useless to try to work out the mean ...
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is it possible to calculate the standard deviation with a given mean and sample size?

I have been going in rounds with this problem... I may be thinking "complicated", any advice? I have the mean and total sample size (=number of data points) and I need to know what is the standard ...
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Step by step correlation calculation

I must understand how I can calculate the correlation for the following probability variables. ...
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Population Standard Deviation

So we know that the population standard deviation $\sigma$ is just the square root of the variance $\sigma ^2$. But what are the uses of the standard deviation? At this juncture it just seems are ...
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Confidence Intervals: When to use what formula. I'm completely confused

I'm working on a few confidence interval questions, each with slight differences that make it very hard to determine what to use. One question asks: An electric scale gives a reading equal to ...
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Variance and Standard Deviation of multiple dice rolls

I'm trying to determine what the variance of rolling $5$ pairs of two dice are when the sums of all $5$ pairs are added up (i.e. ranging from $10$ to $60$). My first question is, when I calculate the ...
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Trouble with samples in a normal distribution

I'm okay with solving regular normal distribution questions (where X is a normal random variable with mean $\mu$ and standard deviation $\sigma$). However, we're currently dealing with samples within ...
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Finding probability 400 components last 5012 or less hours using standard deviation?

The lifetime of certain electronic components is a random variable with the expectation of 5000 hours and a standard deviation of 100 hours. What is the probability that the average lifetime of 400 ...
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Is standard deviation additive?

I am helping someone study for a statistics exam. I am quite good at most other math classes but it's been a while since I studied statistics. I am stuck on one of the exercise problems that we worked ...