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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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
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153,000 | 0.058848
332,641 | 0.36352
506,629 | 0.53
If $x$ being the number of database records ...
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56 views
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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56 views
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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17 views
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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2answers
29 views
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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98 views
to calculate standard deviation using mean and sample size
Given the mean as 1336 and sample size as 24, how to calculate standard deviation when the deviation scores and sample figures are unknown.
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Do data points outside standard deviation persist in data subsets?
I have a data set of dates and values that are being plotted. I create a simple trend line y=a+bx using linear regression, and then I create a 'trend channel' (I ...
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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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62 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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25 views
Underlying assumption of t-test and standard error
I am having a hard time explaining why my significance test based on randomization is different from a t-test.
I have 20 different data points and I know each comes from a Gaussian distribution. I ...
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24 views
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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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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Remove an observation from an standard deviation
I'm calculating the standard deviation in a iterative manner (due to technical restrictions were recalculating the standard deviation obtaining all the observations has a high cost).
A formula to ...
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optimum weights for minimum variance
If $X_i$ is an estimator for $x_i$, and an estimate of the sum i.e. $ Y = x_1 + x_2 + ... + x_n $ is made by the ration $X_i / p_i$ where $p_i$ is the probability that $X_i$ is chosen , then what are ...
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selection for variance reduction in monte-carlo
I need to prove that the following variance reduction operations lead to the optimum value. A related question i asked here about variance reduction gives the optimal proportions are according to ...
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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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Comparing data to find the “consistently lowest” subset of data.
I am currently faced with a set of data representing the time taken to move and click on an object, in relation to the distance and size of the object (see Fitts's Law if curious but that's ...
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2answers
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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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Casino Statistics
I am writing an article on european roulette and I was wondering how much do the owners need to put into the pot in relation to the maximum bet allowed on the table to be able to pay out every ...
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1answer
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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
How do you find the standard deviation of the weighted mean?
The weighted mean is defined: $\bar{x} = \frac{\sum{wx}}{\sum{w}}$
The weighted standard deviation (since it is not specified, I take it ...
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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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Error rate, one main data set compared to test data set
I have conducted tests where I try to improve the latency for different indepentent scenarios.
I have one set a data with values for a year and another set of data for my test period.
The ...
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1answer
262 views
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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Compute a separate, running, weighted standard deviation for above and below the mean?
I'll get right to the problem.
I have a data set that may or may not be skewed. To account for this, I want to keep track of the variance above the mean and below the mean.
I am unable to store the ...
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2answers
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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 ...
