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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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) F(z)=NORMDIST(...
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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Four beans are randomly withdrawn in succession with replacement, and the number of red beans, $X$, is observed.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 ...
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Two questions about normal distribution and its calculation

dear community members, I got this question in my handbook for exam preparation. I was trying to calculate the output but I'm stuck with figuring out the correct value. The question is: According to ...
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Was it really necessary to have the variance be calculated with $\Sigma (X-\mu)^2 $? [duplicate]

From what I understand, in calculating $$\sigma^2 = \frac{\sum (X - \mu)^2}{N}$$ the only reason why the squaring is done is to make distance from mean always positive. So my question, why couldn't ...
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OLS on big data

We regress $Y$ on categorical data $X_1,…,X_p$. This is a large data set (that's right, big data!) but many of the rows of the design matrix are duplicated. We can summarize the data by averaging $Y$ ...
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Normal Distribution and Percentile Word Problem

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with mean ...
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Aggregating standard deviation to a summary point

I have a range of data (server performance statistics) is formatted as follows, for each server: ...
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Variance of Normal Distribution

Consider $X_1$~normal(4,3) , $X_2$~normal(5,7), and $X_3$~normal(6,4), where $X_1$, $X_2$, and $X_3$ are independent. Obtain variance of $W = 2X_1 - X_2 + 3X_3 + 3.$ Attempt : Since we are given $\...
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Chebyshev inequality for standard deviation

everyone! I have a question when I studied matrices of norm and distance. Chebyshev inequality for standard deviation. If $k$ is the number of entries of $x$ that satisfy $$ |x_i - \operatorname{...
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Standard deviations assume a white noise component

"The important point is that these standard deviations assume a white noise stochastic component which will rarely be true for time series." Why do these standard deviations assume a white noise ...
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What is the difference between root mean square, and standard deviation?

I am currently working through the Feynman Lectures, chapter 6: Probability. I have reached his problem of the "random walk". After deriving this and getting some root mean square, wouldn't this ...
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Is Standard Deviation Independent of Sample values

I have a rule to implement which says that if standard deviation of a set of measurements is > x, then y is true. Problem is that my values could be anything like: 1,1.1,1.2,1.2,1.3.. or 100, 100....
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Understanding the Normal Distribution?

If a sample is normal with observations independent and identically distributed: $\mu|\sigma^2 \propto N(\beta \,,\,\sigma^2/\, n_0)$ How can I show that $\mu\,|\,x_1,x_2,....x_n\,,\,\sigma^2 \sim ...
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Estimate of a sample size of a search algorithm

I am trying to estimate the order of the sample size of a probabilistic search algorithm. The problem is the following: I have a counting problem where an oracle can identify the right solution, i.e. ...
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Standard Deviation and Mean using Chebyshevs Theorem

Find the standard deviation and mean when The sale prices of 88.9% of the homes in a certain neighborhood were between \$438,572 and \$189,992. From Chebyshevs theorem it is known that 88.9% is 3 ...
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Variance of discrete random variable

I am trying to refresh my probability theory and got stuck on one question about discrete random variables. Let $\Omega = \{ \omega_1, \omega_2, \ldots, \omega_N \} $ be the set of all elementary ...
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Standard deviation for measurements with errors - least squares?

I have been bugged by a simple problem in statistics recently. Let's assume that I have made a set of measurements of a certain quantity, each with an uncertainty estimate. I have a set of tuples $\{...
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How do I find a percentage with only the mean and standard deviation?

'If we have a set of scores that are normally distributed and have a mean of 20 and a standard deviation of 5, what percentage of scores are greater than 20?' Now I know the answer is 50%, because ...
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AWG Noise and RMS Voltage

A question says, a channel is corrupted by Additive White Gaussian Noise with zero mean and RMS voltage 20 nV. The probability that the noise voltage is less than a particular positive value c is 0.9. ...
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Which is the default Standard Deviation Formula

I have to implement a test from research paper which says: As for testing criteria, standard deviation or min-to-90th percentile ( ) of large packets (1500 B) can be effectively used to find the ...
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I need help with this Standard Uniform random variable problem

Click here for problem image I need help on how to do b,c and d. Can I please have an idea of how to start it because i have no idea how to do this.
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How are the following two Chebychev's inequalities equivalent?

I was looking at the following definition of Chebyshev's inequality $$P(|X - E(X)| \geq r) \leq \frac{Var(X)}{r^2}$$ which includes the expected value and variance of $X$, and then I discovered ...
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How to calculate new standard deviation based on formula given only the mean and set standard deviations

I currently have the mean and standard deviation, I need to calculate the new standard deviation given a formula: ...
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Multivariate Gaussian vs univariate

I am developing a classification task where I generate a gaussian distribution (its mean and standard deviation) from a set of 3-dimensional data. My question is: would the classifier give same ...
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Intuition for why variance of sample means depends only on sample size?

The variance of sample means is given by $\sigma ^2 / n$ where $n$ is the sample size. Interestingly, this does not seem to depend on the size of the population — one would expect that the variance ...
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Curve fit to curve in standard deviation sense.

Two curves $A(t)$ and $B(t)$ are defined by their values on a grid $t = 1,..,T$. The task is to minimize $\sum_{t=1}^TB(t)-(k\cdot A(t)+b)$, where $k$ and $t$ - parameters. I understand, that I ...
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Determine skewness if only mode and median given?

For a given set of data the mean is 10.5 and the mode is 9. What c an we deduce about the skewness of the data? A The data is positively skewed. B The data is negatively skewed. C The ...
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Is this standard deviation calculation correct?

I got an answer of 11.88 but apparently the correct answer is 547. Which part of this solution is wrong?
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Does the standard deviation of a normal distribution change when looking at a shorter period?

Say we are given a normal distribution with mean $\mu$ and standard deviation $\sigma$, where $\mu$ is the expectation in time period $T$. Now, say you need to use the distribution over a shorter ...
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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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Standard deviation help

I'm not sure how to start this question. A brand of rice advertises on the bag that it contains 1kg of rice. The machine that pours the rice however, is not able to exactly pour 1000g each time, ...
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Distribution of ratio of 2 points drawn from normal distribution?

Let's say we have a known normal distribution $N(\mu,\sigma^2)$. I now draw 2 points $p1$ and $p2$ randomly from this Gaussian distribution for every observation, and repeat this process large number ...
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2 simple statistics questions regarding probability and means.

Fire alarms go off in the engineering building an average of 13 times per year. Find the probability of more than one fire alarm going off in the month of December. For this one, I am uncertain on ...
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Probability involving the average of a simple random sample

So here's the question: Maria is shopping for wireless routers and is overwhelmed by the number of options. In order to get a feel for the average price, she takes a random sample of $75$ routers. The ...
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When does it make sense to build a confidence interval for the mean with known standard deviation?

While estimating with confidence interval the mean value for a population, there are two options: If the standard deviation is known, and If the standard deviation is unknown. But in the first ...
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Adding Standard Deviations - Sig figs?

I am working on a question that asks to calculate the answer along with it's standard deviation. The +- symbol stands for the uncertainty. (67+-11) + (6+-4) + (21+-3) + (7+-2); Because this is ...
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Variance of a non-linear function of a random variable

I know that the formula for Variance of a linear function of a random variable is $\textrm{var}(aX+b)=a^2\textrm{var}(X)$ But what about if the function is not-linear? Is there any another formula ...
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Probability normal distribution; changing the SD.

A company manufactures tennis balls whose diameters are normally distributed with mean $67$ mm and standard deviation $1$ mm. The manufacturer wants to change the standard deviation so that $99$...
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Help with understanding point from Nassim Taleb's book “Dynamic Hedging”

This is an excerpt from Nassim Taleb's book "Dynamic Hedging" (a book on option trading strategies) page vii Most examples in this book are presented as generic situations. The volatility will ...
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Recommendation on padding average value

I'm building a progress bar for a web app. I have historical time duration values (eg 5 minutes, 4 minutes, 6 minutes), and then at an interval I get the current duration when something is in progress,...
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Normalizing and dividing mean by standard deviation

I'm trying to develop a metric based on set A and set B where the difference between A and <...
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anything different in conceptual in CI

I have a question about CI, could any one help? Assume $$Y_{n,1}=X_{n,p}\beta_{p,1}+\epsilon_{n,1}$$ suppose $\epsilon_{i}$ is i.i.d for all $i=1,2...n$, with variance $\sigma^2$ Denote the least ...
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Measure for fit quality independent of data set size

I've got a data set, which in the beginning behaves like a straight line, but later it deviates. I would like to determine when the straight behavior ends. To do so I would like to stepwise include ...
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Standard deviation of measured probabilities

I would like to know and understand the answer of this small maths problem on probabilities. I looked around but I don't find the answer and it really bugs me since I need it for my data analysis! I ...