# 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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### Can the mean of the means of multiple sets from a single population give insight into the individual sets or the overall population?

This relates to environmental sampling: I have three composite samples consisting of nine sub-samples each collected from a waste lagoon. Assuming I treat each composite sample result as a "mean" (...
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### Prove that Standard Deviation is always $\geq$ Mean Absolute Deviation

Where $$s = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2}$$ and $$M = \frac{1}{n} \sum_{i=1}^{n} |x_i - \bar{x}|$$ I came up with a sketchy proof for the case of $2$ values, but I would like ...
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### Can I use mean and standard deviation to spot outliers?

I have a list of measured numbers (e. g. lengths of products). Of these I can easily compute the mean and the standard deviation. Now, when a new measured number arrives, I'd like to tell the ...
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### Derivation of standard error of regression estimate with degrees of freedom

I am taking a course of Econometrics: I need help to understand as to how do we arrive at the formula for standard error of regression $$\hat{\sigma}^2=\frac{\sum{e_i^2}}{n-k}.$$ I understand the ...
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### standard deviation above or below the mean [on hold]

The following is data of 10 patients in a hospital 165,135,151,155,158,146,149,124,162,173 If a patient is selected randomly, find the probability his/her data exceeds one standard deviation above ...
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### Is it valid to calculate standard deviation for n=2?

My colleagues and I are having discussion whether it's valid to calculate standard deviation for $n=2$ or not? I think it's valid since I can calculate based on the equation, but higher N will give ...
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### How do I calculate a point estimate of the largest 10%?

Here is the provided data: The question asked is: Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90% and state ...
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### How to maximize Std Dev given a range of possible values, a number of values, and a specific mean?

(I'm asking here and not stats.stackexchange because I'd like a mathematical proof of this) In this question: Prove how to maximize Standard Deviation given a certain mean $\bar{x}$ and set of values;...
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### Prove how to maximize Standard Deviation given a certain mean $\bar{x}$ and set of values

I'm talking specifically of population SD, where $$s = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2}$$ I have a hunch that $s$ is maximized for a certain mean $\bar{x}$ when the values in ...
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### Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
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### Caclulate Standard Error when subtracting two effects

I am working on this issue that compares two regions with the McCrary Test (Regression Discontinuity Design). It basically measures how the density of a variable of interest develops accross a pre set ...
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### The standard deviation is more stable than the mean?

In an introduction to the subject of hypothesis testing, a book on probability and statistics for engineering students has a statement asserting that "the standard deviation is more stable than the ...
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### Does standardizing a random variable that is not normally distributed change the underlying distribution?

For my analysis I am standardizing Response Times, which are usually known to be skewed and are in my data set, using the "classic" standardization method of substracting the grand mean and dividing ...
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### How do you find 1 standard deviation from the center of an ellipse along the 45-degree angle?

I have generated a normally-distributed elliptical cluster of data in Matlab. The center of the ellipse falls at (0,0) and it has a standard deviation of 1 along one principle axis and a standard ...
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### Combining standard deviations - given mean, sample size, and SD of two sets?

I have two groups A and B. I know A and B's sample sizes, mean performances on a test (not their individual scores however), and the standard deviations of A and B. I know how to combine them to find ...
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### Relevancy of standard deviation

I'm a maths student but I'm a bit of a retard when it comes to probability. I have this very basic question in mind : Why is standard deviation defined as the square root of the variance, when surely ...
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### Variance of exponential moving average

I'm not quite sure what the form for the rolling recursive variance should look like. I have that the recursive average is $m_t = \alpha x_t +(1-a)m_{t-1}$. Then would the rolling recursive variance ...
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### Calculating a three sigma limit on data

So I have a list of data points each with their own error (eg. 3 +/- 0.2 units) and I want to determine which of the data points are within 3 sigma. To do this do I just calculate the standard ...
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### Finding the confidence interval of a normally distributed sample

Traffic police monitor the speed of vehicles as they travel over a new bridge. The average speed for a sample of 27 vehicles was 91.29 km/h, with the sample standard deviation being 4.94 km/h. We will ...
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### Establishing the upper and lower bounds of normal using standard deviation

I understand the concept of standard deviations and z-values, but I'm trying to figure out if standard deviations alone are good for establishing the upper and lower bounds for normal. For example, if ...
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### Confidence interval

I have a set of three data that represent the breakdown voltage of a sample. 1. 140 2. 190 3. 140 From this, the sample size is 3, And I calculated the mean which is 156.6. I want to find a 90% ...
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### Is it possible to calculate standard deviation if I have sum of squares and number of samples as input?

I have following inputs Sum of the squares of the numbers. For example if the numbers are $1,4,6$ the sum of squares is $53 = 1^2+4^2+6^2$. And I have the number of input samples: $3$ in this case....
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### Proof for Standard Deviation Formula for a Binomial Distribution

I understand the concept of standard deviation as the square root of the square of the mean of each sample value - the mean of the sample values. Here is the mathematical representation (I've solved ...
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### Gamma function's mean and standard deviation through shape and rate

I'm currently learning how to program neural networks. In the most basic ones, you initialize your matrix with random numbers that are distributed using Gamma function. I'm using a math library, that ...
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### Mean of the deviations from the mean

I ve been struggling to understand the below problem.If I could get help with this problem, it would be greatly appreciated. Consider the data y, y+a, y+2a,….,y+na and the deviations of these ...
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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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### $X$ and $Y$ are standardized r.v.s. Find $a,b,c,d$ such that $Z=aX+bY$ and $W=cX+dY$ are uncorrelated but still standardized.

Let $X$ and $Y$ be standardized r.v.s (i.e., marginally they each have mean $0$ and variance $1$) with correlation $\rho \in (−1, 1)$. Find $a, b, c, d$ (in terms of $\rho$) such that $Z = aX + bY$ ...
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### Questions about Ridge Regression, how to explain the penalty term?

I have read the introduction of ridge regression in https://tamino.wordpress.com/2011/02/12/ridge-regression/. As we know, the equation of OLS is ∥ y − X β &#...
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### How does using one distribution as another's sample size affect variance?

How does using one distribution as another's sample size affect variance? For example, let's say I roll a 6-sided dice and record the number shown. Then, I roll 'that many' 6 sided dice more and ...
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### Cumulative frequency curve effects on change of standard deviation

Given a cumulative frequency curve . If the standard deviation is lower and median remains the same . Is it true to say that the curve will of the above statement will be steeper and pass through ...
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### If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs.

a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time ...
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