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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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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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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1answer
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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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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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27 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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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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2answers
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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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 $\mu$. ...
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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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21 views

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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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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19 views

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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23 views

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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1answer
17 views

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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2answers
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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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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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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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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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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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38 views

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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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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2answers
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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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Geometric Mean of Random Variables

I measure a series of $n$ objects [O_1, O_2, O_3, ..., O_n]. Because those measurements are quite hard to perform, I have quite a lot of measurement error and ...
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1answer
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Standard distribution formulae trick

I am trying to understand the following question. The height of adult males is normally distributed with a mean of 172cm and standard deviation of 8cm. If 99% of adult males exceed a certain height, ...
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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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14 views

Estimate of group standard deviation given pairs of distances

I'm trying to find how much the errors associated with a specific method of estimating a collection of values will decrease, when I add additional data to make a "better" estimate. In particular, ...
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what's the best way to find a central tendency and filter outliners for this given problem?

I'm faced with the following problem: I have a group of Nodes which belong in the same network. They are constantly talking with one another providing services to one another. Suppose nodeA asks for ...
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Finding the Correct Sample Size N to calculate the $SEM$ in a Relative A/B Test with $X \sim B(p_1,n_1)$ and $Y \sim B(p_2,n_2)$

I asked a similar question on Cross Validated but since I'm more interested on the theory behind choosing the right $N$, I decided to also post it here. For the test, I randomly assign users to two ...
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Deal with circular standard deviation

I have a sensor that gives me a direction of the target in degrees with a certain standard deviation and I use a circular probability density function (PDF) to represent probable locations for the ...
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Standard deviation of a normal distribution with arbitrary points

Good day! Im currently dealing with the formula in determining the expected number of real roots of random algebraic polynomial,,, and I want to solve for the formula of the standard deviation. I have ...
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A Gaussian Divided by a Gaussian Equal to A Gaussian Divided by a Constant

I have a neural-network model in which each neuron is associated with an angle $\theta$. Firing rate as a function of $\theta$ is either a Gaussian or a constant. The claim has been made using this ...
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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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What is Bootstrapping in statistics? How can I use it to determine error in the mean, variance, kurtosis and skewness of a data set?

From what I understood from searching randomly is that it has something to do with resampling. What does this resampling mean? Is it selecting random data from a distribution or is it getting data ...
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finding min and max after removing percentage of num values knowing the standard deviation.

I have a question i have some data and i know it's (number of values, min, max, mean and standard deviation) can I know the minimum after removing x% of the total number of values and the maximum ...
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Standard deviation: calculating how polarizing a question is

I'm trying to calculate how polarizing a question is. Let's say I have a question that has 3 possible choices. A certain percentage of people choose a specific answer. Answer a: $30\%$ Answer b: ...
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1answer
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Standard Error for Weighted Values

I want to calculate the standard error for an experimental measurement. The data is stored as a 2D image which is circularly symmetric about a center point. To reduce the data we radially integrate ...
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Comparing Curves

I am trying to compare a company's revenue to some economic indicators such as DJ index and S&P 500 index. I came up with a way to plot the three lines on the same scale. Here's the table. What ...
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How to compare dispersion of data?

From my statistic book, I learn that standard deviation is used to estimate how much the data spread around the mean value. If I have two or more sets of data, for each one, they normalized to the ...