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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Recalculate Standard Deviation

I know how to calculate a standard deviation when given a set of values. You must calculate the mean, then square the difference of each value between the mean to get the variance. Lastly, the ...
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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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Calculating the sample standard deviation

I've been preparing for an exam tomorrow and was doing a past paper when it appears the mark scheme has an answer that I just cannot fathom. The exact question is to "find a 95% confidence interval ...
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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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Calculating uncertainty in standard deviation

I have a distribution with literally an infinite number of potential data points. I need the standard deviation. I generate about a hundred points and take the standard deviation of the points. ...
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942 views

Comparing annualised volatility from monthly and annual data

I fear there is a very simple answer to this question and its killing me that I can't see it. I am interested in calculating historical volatility: I have monthly index values starting in Jan 2005 ...
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what is the unit of the following standardization formula?

If normalization would be to rescale the range of values to scale between $0$ and $1$ as follow: $x^{'}=\frac{x-\min(x)}{\max(x)-\min(x)}$ where the interval of $x^{'}$ is closed between $[0,1]$ ...
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Mean and standard deviation after a coin is tossed

Could someone help solve this? Let X equal the number of heads when $3600$ coins are tossed. Find the Mean and Standard Deviation of X
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How do you calculate the correlation between the intercept's and beta's standard error in a univariate linear regression?

I am running a regression to predict a variable Y as follows: $Y=\alpha+\beta\times x+\epsilon$ I am trying to get a distribution of the expected value of Y given standard errors in the model ...
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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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Does a larger coefficient of variation mean larger variability?

I'm reviewing right now for an exam and I've stumbled across this online reviewer. In the solution for question #2 it stated that Section B is more consistent so there is greater variability in the ...
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487 views

How to calculate standard deviation from mean and probability?

What's the formula to calculate the standard deviation knowing the mean and a certain probability, but not knowing all the n's. http://stattrek.com/online-calculator/normal.aspx For example, ^that ...
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Why do RMS and Standard Deviations sum squares?

I've seen some references to this - or a few examples of it, but for some reason it's not clicking. Can anyone give me a good layman's explanation of why calculations such as RMS values and Standard ...
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Removing outliers from a dataset [migrated]

Assume I have a big dataset (million numbers), and I want the smallest range without outliers. So e.g. I have: $$x=[1,1,50,50,50,50,50,50,50,50,51,51,51,51,10000,10000]$$ I am looking for "the ...
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19 views

Standard deviation and standard error

I have a homework in which I am using data from NFL teams. This information was taken from the ESPN site and I was asked to calculate the following: $mean$, $standard$ $deviation$ and $standard$ ...
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515 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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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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SD probability problem involving chi-square distribution

Preparing for an exam in statistics, I have been pondering the following problem: Given that in country X 14 % of people hold a university degree, find the probability that for random sample of size ...
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According to Chebyshev's rule, how many observations should lie within one and a half standard deviations of the mean?

Using the formula : $p = 1 - k^{-2}$ I calculated that $p = 1 - 1.5^{-2} = 0.56$ , which equals to $56\%$. Because I have $24$ data points I go ahead and solve the number of points is $56\%$ of ...
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Standard deviation and statistics

The concentration by volume of air mixing with methane is distributed with a mean of 20% and a standard deviation of 7%. I want to find the probability that the concentration is less than 30% or ...
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755 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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22 views

Calculating the standard deviation involving a moment generating function

An actuary determines that the claim size for a certain class of accidents is a random variable, X, with moment generation function: $$M_X(t)=\frac{1}{(1-2500t)^4}.$$ Calculate the standard deviation ...
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460 views

Estimating population standard deviation with sample standard deviation

At 4:30 of this video the author decided to estimate the standard deviation of the population with sample standard deviation (sample size was $100$). In the next video, the author mentioned that it ...
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Standard deviation of the mean of sample data

I can't quite understand what this formula means: $$\sigma_{\overline{x}}=\frac{\sigma}{\sqrt n}$$ I know what standard deviation $\sigma$ is - it's the average distance of my data points (samples) ...
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What do I plug in for the z score?

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The ...
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How do I find the $Z$ value and calculate the $P$?

Please DO NOT answer the question, as I just need the right formulas in the form of plugging the numbers from the word problem into it. I struggle with this. And I need to find what the percentage is ...
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Ratios of median/mean and standard deviation/IQR in a normal distribution

I have some queries on the following question For a normal distribution, find the ratios of: (a) $\frac {\mbox{median}}{\mbox{mean}}$ (b) $\frac {\mbox{standard deviation}}{\mbox{interquartile ...
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Normal Distribution, percent less than mean minus one std. dev

GRE Question, part b. My answer is 16%, but the book says 15%. Why? mean = 65 cm stdev = 5 cm Probability that penguin chosen at random will be less than 60 cm is 16%, it shows in Normal ...
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Determine the standard deviation for statistical hypothesis testing when not explicitly given

I have got a video in grayscale, and I am interested to find out if the intensity of a pixel at a given location is more or less constant over time. I have been told here that I can use linear ...
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Standard Deviation vs Population Standard Deviation

In GRE study guide, it gives difference between standard deviation and sample or population standard deviation. I understand the mechanics of this, i.e. in standard deviation you divide all ...
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21 views

Normalize a list of standard deviations

I have several columns of features that I need to normalize to values between 0 and 1 (or -1 and 1, etc.--just something standard) in order to do regressions using ML algorithms (such as SVR, KNN, ...
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Standard deviation problem for short cut technique

Revised-GRE QUESTION I know how to evaluate the standard deviation and mean and also I have basic knowledge about the bell curve. But whenever I have to solve some problems related standard ...
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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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Standard deviation without square

For $(x_i)_{1 \leq i \leq N}$, the standard deviation is of course $$\sigma = \sqrt{\frac{1}{N} \sum_i (x_i - m)^2},$$ where $m$ is the mean value of the $(x_i)$. We can say that the variance ...
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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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Standard deviation of less than one

How would I find the approximate percentage of values within a standard deviation of less than one on the normal model? Chebyshev's rule is only used when the standard deviation is greater than or ...
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Specific confidence intervals question

As of now, I completely suck at computing confidence intervals, and I have an exam in a couple of days. The exact question is as follows: Some people are trying to measure a certain parameter ...
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Why the standard deviation of the sample mean is calculated as $\frac{\sigma}{\sqrt{n}}$?

According to Wikipedia, the standard deviation of a sample mean is calculated as follows $$\frac{\sigma}{\sqrt{n}}$$ Why is that? Why do we need to divide the standard deviation of the population by ...
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Formula for standard deviation

So I am studying for a final exam and I know, or thought I knew, the formula for standard deviation. I quadruple checked in my notes and the slides for the lecture and see that the formula for the ...
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Did I equate the standard deviation correctly?

This was for a frequency table, so I will start from finding the mid points. For standard deviation, find the squares of the midpoints then multiply them by the frequency 7500.5², 12500.5², 17500.5², ...
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Is there a lower bound to the standard deviation of a Gaussian (Normal) distribution?

A Gaussian or Normal distribution is defined by the probability density function $$ f(x \; | \; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} } $$ with $\sigma$ as ...
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Standard Loss Function L(z)

z is the standard normal distribution F(z) is the probability normal distribution L(z) is the standard loss function i can find these values using below code in the excel z=NORMSINV(x) ...
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Finding the variance of a group data set

Okay, so this is what I have so far for the means of these numbers. At this point I've added so many numbers together that my calculations are getting messed up. I need to know how to find the ...
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How do I find the variance for a group data set?

Okay, so this is what I have so far for the means of these numbers. At this point I've added so many numbers together that my calculations are getting messed up. I need to know how to find the ...
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A jar contains seven red and three green beans.

Four beans are randomly withdrawn in succession with replacement, and the number of red beans, $X$, is observed. Determine $\mu$, $\sigma_2$, and $\sigma$ for the random variable $X$. I'm not ...
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How do I find the variance for a range of numbers?

Basically, my homework is asking me to find the variance based on a frequency table. But the frequency table looks like this: Frequency Table: Salary Number of Employees 5,001–10,000 8 employees ...
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How do I find the variance for a range of salaries?

For instance, if I am looking at a frequency table and it says that 6 employees make between 5k-10k, 5 employees make 12k-18k, and 3 employees make 20k-25k...how would I find the variance if the ...
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Am I on the right track with this question on standard deviation?

The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean? ...
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Question about checking normal distribution and analysing confidence intervals

I've got another question about normal distribution and its confidence intervals interpretation. Your explanation will respectively help me to better prepare for my examination. One of the social ...