# Tagged Questions

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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### 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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### Motivation behind standard deviation?

Let's take the numbers 0-10. Their mean is 5, and the individual deviations from 5 are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 And so the average (magnitude of) ...
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### Sample Standard Deviation vs. Population Standard Deviation

I have an HP 50g graphing calculator and I am using it to calculate the standard deviation of some data. In the statistics calculation there is a type which can have two values: Sample Population I ...
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### How can the standard deviation be interpreted when the range is partially impossible?

After meassuring the answer time of a software system I calculated the standard deviation from the samples. The average time is about 200ms, the standard deviation $$\sigma = 300ms$$ According to the ...
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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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### 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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### How can I calculate “most popular” more accurately?

I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ...
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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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### 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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### 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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### Correct Intuition? Standard Deviation and distance in $n$ dimensional space.

Basic Question Is there an intuitive explanation of standard deviation in terms of Euclidean distance in $n$ dimensional space? Longer Version of Question To begin a more detailed sketch of my ...
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### Sample standard deviation

Give a set of 3 integers between 1 and 9 that would give a) the smallest value and b) the largest value of s (sample standard deviation) and find the value of s: i)if repeats are allowed and ii)if no ...
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### What is the maximum value of the sum $\sum_{i=1}^L(\bar{x}-x_i)$, in this specific case.

Let $x_i$ be a positive real variable, with $i=1,2,...,K$. We denote by $\bar{x}$ the average value of the values $x_1, x_2,...,x_K$. Let $a=\min_i x_i$ and $b=\max_i x_i$, then $x_i \in [a,b]$. My ...
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### 95% Confidence Intervals

I was solving this problem from a textbook In a random sample of three pupils, $x_i$ is the mark of the $i$th pupil in a test on volcanoes and $y_i$ is the mark of the $i$th pupil in a test on ...
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### Variance is the squared difference - why not to the 3, or 4 instead?

So there is this question about why variance is squared. And the answer seems to be "because we get to do groovy maths when it is squared". Ok, that's cool, I can dig. However, I'm sitting ...