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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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 ...
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Variance of a max function

Say $x_1$ and $x_2$ are normal random variables with known means and standard deviations and $C$ is a constant. If $y = \max(x_1,x_2,C)$, what is $\mathrm{Var}(y)$? Well, I forgot to tell that $x_1$ ...
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Calculate standard deviation from ratio of two variables

Ok here is my problem. For my research I am investigating if we can use twitter to create sports data. One part of the problem is for example this: We now for example that in the 6th minute of the ...
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Mean equal to standard deviation, with positive values

I read the question and the answers regarding the idea of the mean being equal to the standard deviation, in which the mean can always be adjusted to equal anything. But, if the data is restricted to ...
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1answer
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When standard deviation is unknown?

I am reading a book about Statistics and I have encountered a text line: ...except in the case where standard deviation of the basic set is unknown... I am not really sure what it means, could ...
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915 views

calculate standard deviation from percentage of mean occuring.

I'm not a math person, although I find it quite interesting. I'm a programmer but I've got a math problem I'm trying to figure out. Lets assume I'm trying to create a program that will predict at ...
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327 views

Error Metric which incorporates both mean & standard deviation of data in euclidean space

For simplicities sake (the actually problem is more complex)...Let say I have a set of n 3d points, whose position move over time. For all pairs, I have calculated the mean and standard deviation of ...
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Simple question on standard deviation and mean.

This question has kinda stumped me: For a data set, the mean is 5 and the standard deviation is 1. There are 10 values in the data set. Is the range of the data set bigger, smaller or equal to ...
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323 views

Add value to known mean and Standard deviation

I have a distribution that will continuously have numbers added to it as they are measured. I want to keep only knowledge of the mean, the standard deviation, and the number of values so far in the ...
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significance test

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
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Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
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Calculating minumum representative sample

Let's say I played 500 hands in poker and earned 345 units ( dollars not, important for calculation). So on long term I'm earning 345/500 = 0.69 * 100 = 69 every 100 hand session. But 500 hands is ...
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423 views

Error propagation and averages, a practical question

Ok, I'm sure this is simple, yet I'm confused. Lets say my goal is to obtain an average concentration C=N/V so I take a number of N and V readings with errors: $N_1=50\pm2, V_1=100\pm4$ ...
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101 views

standard deviation computation

If I currently have a sum of N elements (I don't have the elements them self), their mean and the corresponding standard deviation. Later on I receive M (known) other elements. I want to update the ...
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How do i scale my errorbars when i scale my data?

I am plotting distributions of data with the standard deviation and median of my data. Now when i want to scale my median by a another variable, how do i need to modify the standart deviation?
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Normalizing a matrix using matrix operations

I need some help in normalizing my matrix. I have a 5X4 matrix A. I want to normalize each column. Following is the explanation on the operations B = Operation of matrix (A) B matrix is 5x4 matrix. ...
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Standard Deviation: Why divide by $(N-1)$ rather than $N$?

The forumlae for standard deviation seems to be the square root of the sum of the squared deviation from mean divided by $N-1$. Why isn't it simply the square root of the mean of the squared ...
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Multiplying two averages, what to do with the deviations?

If I multiply the averages of two sets of data, then what can I conclude with the deviation of that data? That is, for a given average X1 and X2, both are different sets of data but related, I ...
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Getting the correct error for a mean calculation

A constant k needs to be calculated including its gaussian error. $k = f_{(u,t)}$ $k_i$ can be calculated with the values and errors of $u_i$ and $t_i$ and their respective errors. Main issue is ...
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Prove one standard deviation lies on inflection points

Is my conjecture correct that one standard deviation lies on the inflection points of the normal distribution curve (of the probability density function)? How can it be proved using the standard ...
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Determining variance from sum of two random correlated variables

I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated? ...
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108 views

Estimate the sample deviation in one pass

We've learned this algorithm in class but I'm not sure I've fully understood the correctness of this approach. It is known as Welford's algorithm for the sum of squares, as described in: Welford, ...
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59 views

Set of numbers given, find mean and SD of the other

A set of eight numbers has mean 5 and SD 4. The number 21 and another integer n are added to the set. The standard deviation of the set is now 6. Find n and the mean of the set now.
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642 views

Normal distribution involving $\Phi(z)$ and standard deviation

The random variable X has normal distribution with mean $\mu$ and standard deviation $\sigma$. $\mathbb{P}(X>31)=0.2743$ and $\mathbb{P}(X<39)=0.9192$. Find $\mu$ and $\sigma$.
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What does it mean if the cumulative normal = 1?

What is the significance of cumulative normal = 1? I am trying to program a game, however I have inherited code from another programmer. He is using the cumulative norm. his code is outputting a ...
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incremental computation of standard deviation

How can I compute the standard deviation in an incremental way (using the new value and the last computed mean and/or std deviation) ? for the non incremental way, I just do something like: ...
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What does it mean to divide by the standard deviation?

I'm trying to variance normalise an image, in order to do so, I subtract the mean from the pixel value, to have a 0 mean, and divide by the standard deviation, to have a unit variance, right ? but ...
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How can I compare two averages of imperfect measurements, with their std. deviations?

I have a process by which I measure the times it take to do something, (run some code), and this time varies, a lot. I'm trying to optimize this code, making small changes that sometimes have small ...
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Normalising Standard Deviation as score for Burstiness calculation

I have measured the frequency of terms within the same period (say 14 days), and I wish to use Standard Deviation to calculate their burstiness (i.e. which terms are more spiky), therefore, if a term ...
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615 views

Standard Deviation algorithm for small population size?

I need to calculate the standard deviation on the entire population. The population size is 7, but for others it may be between 5-14. I see a few variance algorithms listed on Wikipedia. What stdev ...
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Course Grade - Statistics Question

I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows: ...
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Variance over two periods with known variances?

If period 1 has variance v1 and period 2 has variance v2, what is the variance over period 1 and period 2? (period 1 and period 2 are the same length) I've done some manual calculations with random ...
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Generate a set of random numbers with a normal distribution

I am trying to generate a set of N random numbers where the set has a normal distribution. I'm currently using a brute force approach: Randomly select N numbers from a normal distribution. Check ...
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864 views

Standard deviation calculation not matching up

I was looking up how standard deviations work, and tried to do it by hand, but what I'm getting isn't matching up with what I have in SQL Server. My population is: 1,2,3,4,5,6,7,8,9. I end up with ...
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Effects of subtracting numbers in a set of random variables on their mean and standard deviation

This is a question about linear combinations of independent random variables. X and Y are independent random variables. $X$ has mean 2 and standard deviation 4. $Y$ has mean 3 and standard deviation ...
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Help with problem: Estimated Standard Deviation of Regression Equation (Simple Linear)

This is a practice problem. I've solved part (a). I have provided verified answers (from the published key) to all parts (a), (b) and & (c). I need help solving (b) and (c). Consider a simple ...
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Financial Calculator HP 10bII - Standard Deviation with Probability

I have a financial calculator and am trying to use it to calculate the standard deviation when probability is involved. For a standard deviation question say on the numbers $1$, $5$, $6$, $10$ ...
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Why is there not a simpler way to calculate the standard deviation?

Steps of getting standard deviation. http://www.techbookreport.com/tutorials/stddev-30-secs.html: Work out the average (mean value) of your set of numbers Work out the difference between each ...
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Charting Histogram Averages and Standard Deviation

Pretty basic question I'm sure: I have a 100 histograms, they are all created from randomly sampling the same data 100 times. Now, I want to show the 'average histogram' with markers at +1 standard ...
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Standard deviation of a rate

I am trying to measure the throughput of a network. I collected sample transfer times for 1,000 trials, and then calculated the arithmetic mean and standard deviation for the data (e.g., mean = 0.2s, ...