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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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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421 views

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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479 views

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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796 views

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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423 views

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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132 views

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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142 views

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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271 views

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 ...
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80 views

Standard error of a statistic

the standard error of a standard deviation is given as : s/n^(1/2). Would the standard error of kurtosis and skewness follow the same idea? For example, se of kurtosis = kurtosis/n^(1/2)?
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averaging STDs vs. calculating a single STD

I have a set of data points. I extracted the Standard Deviation for the whole set, and also extracted STDs for a partition of the points where each element of the partition has at least two points. I ...
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Relation of mean of standard deviations and standard deviation

Let $\{x_{i,j} : i=1..7,j=1,..n\}$ be a set of samples from $n$ weeks (where $i$ denotes the day of the week). Is there any interesting information to be gleaned from the relationship (ratio, ...
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Moss scheduling Simulator and Standard Deviation in plain english?

source : http://www.ontko.com/moss/sched/user_guide.html Configuration File Options standdev n * The number of standard deviations from the average length of time a process should execute ...
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rate of convergence of mean ,variance & skewness estimators

We are asked a question which of mean,variance or skewness converges faster. At first I thought it was straight forward answer: mean->variance->skewness. But I am not sure anymore because I read ...
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Average, standard deviation and min/max values

I'm analzying a computer science paper and just found in the experimental setup the following statement: Average (standard deviation) of number of files per peer: 464 (554) Min - max number of files ...
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flares probability

There are 33 no of flares distributed in 2 hemisphere north and south. the no of flares in north hemisphere is 14 and no of flares in southern hemisphere is 19. then how to find the probability of ...
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Calculating missing data points from standard deviation and mean

I have to figure out what to missing data points are from a set of 10 scores. The mean of the 10 observed scores is 20.0 and the standard deviation is 6.0. The observed scores are listed below, with ...
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Mean and Standard Deviation

I've been struggling to solve this problem for quite some time. The solution states that the mean = 0,4% and SD = 2,5%, but I can't understand why. "The daily return on a stock has a mean of 0,2% and ...
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How to interpret standard deviation of samples with different means?

Let be two samples collections A and B. Mean of the first is 5 and the second is 15. Standard deviation of the first is 2 and the second is 5. Can we conclude something even though the two datasets ...
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Which is a better measure of uncertainty: standard deviation or resolution uncertainty?

Let's say I take a ton of measurements of the diameter of a marble with a 0.001" resolution micrometer, and I calculate the standard deviation of the sample set. Would the standard deviation be a ...
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Given a set of data (distance vs time) obtain a closer approximate for velocity

This is actually a physics experiment. I've collected a set of data Distance and time it takes for a cart to move down an incline plane. From here, I've calculated the average time (...
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Standard Deviation vs Standard Error

I am confused about the difference between standard deviation and error. When do I use which? From my lecture: Standard deviation quantifies spread of data about mean Standard error measures spread ...
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Continuously sampled event: Estimating the value of a future data point, based on past measurements and their tendency

Problem I'd appreciate some ideas on how to define a formula to estimate the value of a future data point for a continuously sampled event, based on past measurements and their tendency. At any ...
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Meaning of Empirical formula when applied to some cases

When applying the Empirical formula on a data set, for example calculating 1, 2 or 3 standard deviations below and above the mean of a data set, for some cases, this might not make sense. For example, ...
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Adjusting mean and standard deviation

There's a set of 8 bags with the following weights in grams given: 1013, 997, 1013, 1013, 1004, 985, 991, 997 The mean is 1001.625, unbiased standard deviation is 10.86. I have the following ...
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Need to calculate significance from a data set.

I have a set of data that looks like this: ...
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Extracting a function from a standard

I have a standard and I need create a function to resolve this, for example: if my $X < 21$ my $Y$ will be $24$ else if my $x < 28$ my $y$ will be $32$ ... How do I calculate a function for ...
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Statistics - Z-score confusion.

For z score, you are taking the sample value subtracting population mean and dividing it by std deviation. Is that correct so far? Now, the "sample value" is defined by an equation. In my scenario, I ...