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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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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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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Percentile for a Given Z-Score

Disclaimer: Statistical math person I am not... I'm a programmer that has been tasked with finding the percentile a child will fall in depending on their weight and age according to the CDC. The ...
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27 views

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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126 views

Finding 'symmetrical range' from mean.

A machine used to make butter where its masses are normally distributed with mean m and standard deviation s.It is found that 5% from these butters are having mass more than 85g where else 10% are of ...
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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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18 views

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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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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How to choose the degree of freedom when calculating the variance var(X)?

I have seen in the text books that sometimes while calculating the Variance of a set of numbers $Var(X)$ = $\sum_{i}^{n} \frac {(x_{i}-\mu)^2}{n}$ also $Var(X)$ = $\sum_{i}^{n} \frac ...
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441 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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425 views

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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Variance decomposition of double sum

This question is about the variance decomposition of a double sum. For a single sum, it is well known that: ...
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28 views

Exponential Probability - Light bulb lifetime question

Suppose the lifetime of a cheap light bulb is exponentially distributed with average lifetime equal to 100 hours. If you have a supply of 100 such bulbs and you use one at a time, with a failed one ...
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761 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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1answer
26 views

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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How many experiments i need to make if i want to find out expeted percentage error of method?

There are two approaches to measure certain attribute X in set of N samples. First one always gives you for sample #n true value of sample's attribute - Xn(true). Second approach gives you for sample ...
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24 views

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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527 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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306 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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418 views

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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23 views

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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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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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 $\mu$. ...
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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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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 ...
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Isolate Sigma and FWHM from gaussian

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 ...
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365 views

why the standard deviation is not as the same as online calculator

I need to calculate the standard deviation for these numbrs: -12 -3 0 -13 8 -6 0 -22 -1 7 -7 1 -2 -13 -4 0 -6 -4 -10 3 I did everything, but still my answer is ...
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61 views

Bootstrap method failing where blocking works

I'm computing an average of individual samples that are not entirely independent and need an estimate for the true standard deviation. According to Newman and Barkema's book the most reliable method ...
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36 views

Standard Deviation comparison

Currently i am working on my master thesis. I performed a research of the weather on sales. Different weather types are included in the model such as sunshine duration, duration of rainfall and level ...
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24 views

Statistics,standard deviation,spread,gemoetric meaning

What are the geometrical interpretations/meanings of these statistical quantities: mean, standard deviation and spread?
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57 views

How to perform mathematical operations using mean and standard deviation.

It's given that a particular parameter, say base-time $T_b$ follows a lognormal distribution with the mean of $10$ years and the standard deviation of $5$ years. Now, how do I estimate the value for ...
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Converting one normal distribution to another

I have a long data similar to this; between 15 and 25 consider its mean as m and calculated standard deviation using this formula. I assumed the above data as a normally distributed data and can ...
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Portfolio sd, covariance over different time periods

So we are trying to forecasted portfolio return and deviation of a historic set of investments, we have different lengths of data for different investments. My boss calculated the covariance using the ...
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studying set I of population

let x be the mean and € the standard deviation of the statistics ×1,,,,,,, xn. let I=(x-3€, x+3×€) and the number of items not in I is k. prove that n greater or equal to 9k. prove that the ...
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How to reduce the standard deviation from $P$ where $P$ involves a random integer uniformly distributed in $\left[ 0,100\right]$

I have a probability $P$ derived from: - A random integer $A$ uniformly distributed on its range such that $A\in\left[0, 100\right]$ - An integer $K$ such that $K\in\Bbb N$ - A number $X$ such that ...
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What to call & how to compute errors in a very asymmetric sample

Consider the following sample $\{1.25,1.5,1.75,2.0,2.25,2.5,2.75,10.\}$. Mean is $\mu=3.$, standard deviation is $\sigma\approx 2.69$. I am wondering how to compute and what to call error bars in the ...
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What is meant by statisticians when they talk about between population differences vs within population differences?

Suppose we have two populations of people in different parts of the world and we want to talk about the variation in heights between the two populations. As I understand it, statisticians are talking ...
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A casino owner is concerned based on past experience that his dice show 6 too often

Currently I am trying to understand hypothesis testing, but I have a problem with the following question: A casino owner is concerned based on past experience that his dice show 6 too often. He makes ...
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37 views

Statistics- Finding Probability

A local lawn service has determined the average time it takes to mow an average residential yard is thirty-five minutes. If mowing times are independent and constant, what is the probability it will ...
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248 views

Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...
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Statistics of several small datasets

I have 3 different datasets, each with 5 datapoints with a certain error. In theory, all the datapoints should have the same value, even from the different datasets (So, ideally I end up with 15 the ...
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Will calculating standard deviations from percentages give different results to claculating them from the raw data?

I'll start off by saying I am not a mathematician, nor have I studied maths for many years, so please keep the answers simple :) I am working with data that has a geographical context. So assume I ...
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Probability involving Normal Distribution

Two instruments are used to measure the height, h, of a tower. The error made by the less accurate instrument is normally distributed with mean 0 and standard deviation 0.0056h. The error made by the ...
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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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Why do statisticians like “$n-1$” instead of “$n$”?

Does anyone have an intuitive explanation (no formulas, just words! :D) about the "$n-1$" instead of "$n$" in the unbiased variance estimator $$S_n^2 = \dfrac{\sum\limits_{i = 1}^n ...
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How do I calculate if a line on a graph is generally far away from another line?

disclaimer: I'm (evidently) not a mathematician/statistician and a total n00b so if this question is too basic for the community let me know! Also excuse any misuse of terminology! Say I have two ...
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Sum of Two Normal Distributions - Weighted?

The problem is given as such: John owns a portfolio with two stocks, ABC and XYZ. He has invested \$400 in ABC and \$600 in XYZ. The quarterly return on ABC is normally distributed with a mean of 7% ...
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Removing slope from running times

First of all, & looking at the suggested question list, I hesitate at asking this basic question: Here goes. I'm trying to assess my fitness, and I need a bit of mathematical help. I do a little ...
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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 ...