# 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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### 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 ...
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### Calculating the Standard Deviation

So I'm doing some homework and I'm really struggling trying to figure out how to calculate the standard deviation. It's my understanding that to get it, you need the variance, but apparently I'm doing ...
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### Calculating the absolute minimum (average) deviation

If a set of numbers were: $\{0;1;2\}$ the mean would be equal to $1$ and so the absolute average deviation would equals $1$: $\frac {(1-0)+(1-1)+(2-1)}3=1$ But if the set of numbers were: $\{0;2;2\}$ ...
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### Standart deviation of a hypergeometric distribution

So, here is the problem, I have 40 green marbles and 60 red marbles. 20 marbles are taken without replacement. Determine the standard deviation of the number of green marbles taken. I used the ...
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### Choosing between several methods to replace bad or missing data.

We are doing some quality control on data coming in from stations all over the world. Part of the quality control involves testing the data on several different things like plausibility, etc. If a ...
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### Normalize graphs to a specific heigh

I have the below graph generated in excel And I want to normalize the 4 curves to have the same height. I want their peaks to be at the same height as the "Average" curve, after normalization. Can ...
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### Calculate new variance when sample size increases

Suppose I have 10,000 data points with the following statistics: Sample mean: 7 Sample variance: 4.2 (and hence standard deviation 2.05) Population mean is also 7. Now if I increase the sample ...
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### Will the mean equal the standard deviation

In my problem, there are three classes that have each taken a test and in these classes, there are 99 students. Class A had 1 student who scored a 1, 1 students who scored a 99, and 97 students who ...
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### Standard deviation of flipping coins

My question deals with flipping a coin. I figured out that in one session of flipping a coin 400 times, the standard deviation for a 95% confidence interval is 20. I understand this to mean that (95% ...
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### How to find the +/- error of a radial average?

I have a set of directions in degrees in which I want to find the average and the distribution error. At the end of the day, I want to say something like: "Given these 100 directions, the average is ...
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### How to find a data value using only standard deviation?

I have a homework problem with the following data values: x, 17, 24, 13, 21. I need to find x, but I do not have the mean. I only have the standard deviation, which is square root of 14, or 3.745. How ...
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### Difference between these two standard deviation formulas?

Today I started reading statistics and I came across these two S.D formulas: $$\sqrt{\frac 1 n \sum (X - \overline X)^2} \textrm{ and } \sqrt{\frac 1 {n-1}\sum (X - \overline X)^2}$$ What is the ...
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### Approach to build multivariate ranking system?

I have data of various sellers on ecommerce platform. I am trying to compute seller ranking score based on various features, such as 1] Order fulfillment rates [numeric] 2] Order cancel rate [...
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Is it true that to change the mean and stdev of a normal distribution (with mean 0 and stdev 1), all one has to do is to multiply the current PDF by the new stdev and add the mean? I.e. I have N(0,1),...
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### Find the time offset using standard deviation

maths is not my strong point so I am trying to make sense of this. Basically I have a thermal camera that takes pictures many times a second. This camera has an internal clock that records a time ...
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### How to compare standard deviations of different sample sizes

I am interested in estimating the value of an unknown, random variable, X. X changes over time. So, X = X(t) = Xt At specific time intervals, I estimate the value of Xt using 7 different methods. Some ...
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### How to calculate two populations combined mean and standard deviation.

I'm trying to solve following type of combined date given question. Imagined that there's two factories. They are X and Y. "X" factory has 10 workers and "Y" has 20 workers. These two factory's ...
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### Standard deviation misunderstanding

Here is a question that I stumbled upon (and the solution to it, my reasoning follows after the image): I answered "The two quantities are equal". My reasoning was as follows: the question mentions ...
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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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### Variation test for Poisson distribution

I have two groups of data following Poisson distribution. I want to check if the two groups have the same variation (or if variation of one group is larger). I know F-test can be used to do this, but ...
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### Standard deviation of the product of gaussians

What is the standard deviation of the product of two random variables that each have Gaussian Distributions? I don't even know where to begin on this problem.
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### Normal distribution with standard deviation = I

Suppose a vector $\epsilon \in \mathbb R^d$ is a random vector drawn from the isotropic normal distribution: $\epsilon$ ~ $\mathcal N (0, I)$ [As in Eq. 1.34 here.] I suppose ...
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### How does the formula for standard deviation result in the normal distribution

Trying to understand this is in a high school level. I understand that the how $\frac {\Sigma|x-\bar x|}{n}$ calculates the mean of the distances of each score to the mean. I use this idea to map ...
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### 3-sigma approximation

I am making a system involving a sensor who has to be really precise. I found on their datasheet a diagram that shows the typical performance of the sensor. There's the mean value, the +3 sigma, ...
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### Calculating cumulative error in distribution of elements

I am dealing with a real life situation where I have a distribution of 12 unique elements that can be permutated in any way possible (so 12! = 479,001,600 possible permutations). The index position ...
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### By how much does the mean and standard deviation change over a certain amount?

The monthly profit of a small convenience store is a random variable with mean μ = 100 000 and standard deviation σ = 6 000. If we define Y to be the profit per year, assume that the monthly profits ...
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### How many points necessary for standard deviation?

First off, I'm not a mathematician, and never took statistics in college, what I know about standard deviation I've learned in the past few weeks, so be gentle... I'm working on a piece of software ...
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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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### Finding standard deviation given joint probabilities

I'm trying to find the standard deviation of $Z = X + Y$ given the following table: I'm getting $E[Z^2] = 36.31$ and $E[Z] = 5.45$, giving me a variance of $Var[X] = 36.31 - (5.45)^2 = 6.6075$ ...
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### Probability distribution; what is probability that i wont spend more than 75% of the customers

Very simple question but I am kinda stuck. Suppose that evidence in sales data suggests that average amount spent by a customer in a store averages 35.60 with a standard deviation of 16.4. A sample ...
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### Definition of standard deviation and $l_2$

If we denote the mean as $\mu$, then the standard deviation is: $$\sigma\equiv\left(\sum_{x\in X}{p(x)(x-\mu)^2}\right)^\frac{1}{2}$$ In other words, $\sigma$ is the average $l_2$ distance from $\mu$. ...
### How to find the minimum of $f(a_1, b_1, \ldots , a_m, b_m) = \sum_{j=1}^{n} (y_j - \sum_{k=1}^{m} a_kx_j^{b_k})^2$?
$$f(a_1, b_1, \ldots , a_m, b_m) = \sum_{j=1}^{n} (y_j - \sum_{k=1}^m a_kx_j^{b_k})^2$$ $$2m < n$$ $x$ and $y$ are constants, and $a$ and $b$ are variables to find. I took deviation out of it and ...
I have the Gaussian: $a e^{-b^2 (x-c)^2}$ And need to isolate the Sigma and FWHM from it. I believe that $b = \frac{1}{\sigma^2}$ and $FWHM = 2.354(\sigma/2)$ However, I need to program this ...