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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Formula to get mean and standard deviation of this multi-variable equation

$$ \binom n x \times\left(\frac1r\right)^x\times\left(\frac{r-1}r\right)^{n-x} $$ If you have $n$ boxes and have a $\frac1r$ chance to fill each one, this equation returns the chance that you fill ...
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CV Percentage Error with Confidence Variable

I am trying to calculate a confidence variable (CV %) of two numbers where the numbers them selves have a confidence range. Appologies for my sloppy representation, I am somewhat of an equation novice ...
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What is the maximum value of the sum $\sum_{i=1}^L(\bar{x}-x_i)$, in this specific case.

Let $x_i$ be a positive real variable, with $i=1,2,...,K$. We denote by $\bar{x}$ the average value of the values $x_1, x_2,...,x_K$. Let $a=\min_i x_i$ and $b=\max_i x_i$, then $x_i \in [a,b]$. My ...
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Are there any limits on Standard Deviation of a data set with given $n$ and mean?

Say a class of 200 students is graded out of 100 marks. The mean of the dataset is 50. Can we put a maximum limit on Standard Deviation for the set ? I thought of putting a number of people onto 100 ...
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Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ...
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34 views

Discrepancy between different methods for finding standard deviation?

I can't see where I am going wrong. There are two different ways of writing the standard deviation: $ \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i – \overline{x})^2}$ $ \sigma = ...
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Trouble understanding when to use ANOVA to analyse variances?

I'm having trouble knowing when to use the ANOVA method for analysing variances. For example this question: $1.$ In an investigation of the effect of large amounts of lime on marigolds, the numbers ...
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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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81 views

Standard Deviation: Population versus Sample (specific example)

So, I'm trying to use a t-test to test a hypothesis regarding information: My students were given a question in which they chose either $1, 2, 3, 4$, or $5$ to determine how much they enjoyed my ...
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154 views

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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Lower std.deviation of a distribution?

How would one lower the std.dev => $\sigma$ for an arbitrary distribution? The reason why I ask, is because I have a distribution which tend to get far above my threshold value, and i am running out ...
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112 views

Calculate mean and std.dev from a lot of coordinates

How do i calculate the mean coordinate and the standard deviation of a cloud of (x,y) coordinates. I know how to calculate the mean, but i am struggling with calculating the std. deviation.
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Probability mean,variance and standard deviation formula confusion.

I have a confusion in the formula attached. Why and how are the two formulas equivalent ? sigma in the image is the standard deviation of a distribution...
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1answer
58 views

Width of Gaussian distribution from N trials of coin tossing

What is the width of the Gaussian distribution that is generated from performing $N$ trials of coin tossing? Example: In a trial of 1000 tosses of a coin, $P(H)=0.5$ and $P'(H)=0.5$, where $H$ refers ...
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218 views

Chebyshev's inequality for 1 standard deviation results in 0?

In applying Chebyshev's inequality to a probability distribution, the following is the given equation: $$p(\mu - c*\sigma \le X \le \mu + c*\sigma) \ge 1 - \frac{1}{c^2}$$ This indicates for any ...
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1answer
40 views

Method for determining the average deviation of data values over time?

I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet. For convenience, I've set the minimum and maximum values on the y-axis to the weights that ...
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Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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890 views

Finding the probability of loss from standard deviation in normal distribution

I am unsure how to approach the following question. The returns from a project are normally distributed with a mean of \$220,000 and a standard deviation of \$160,000. If the project loses more than ...
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797 views

geometric standard deviation

The geometric mean is like the arithmetic mean on a log scale. with the arithmetic mean it is often useful to find the standard deviation. Can the same sort of thing be done to create a geometric ...
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52 views

Calculate Sample standard deviation and MAD

I need to solve this problem for an arbitrary N. I'm not exactly sure how to go about this. I have formulas to calculate both standard deviation and MAD, however I'm not sure what to do with the ...
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1answer
46 views

Showing $s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2=\frac{1}{n-1}\left [\sum_{i=1}^n x_i^2-\frac{1}{n}\left ( \sum_1^nx_i\right )^2 \right ]$ [duplicate]

I've got as far as this $$s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2=\frac{1}{n-1}\sum_{i=1}^n\left ( x_i^2-2x_i\bar{x}+\bar{x}^2\right )$$ $$=\frac{1}{n-1}\left ...
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95% Confidence Intervals

I was solving this problem from a textbook In a random sample of three pupils, $x_i$ is the mark of the $i$th pupil in a test on volcanoes and $y_i$ is the mark of the $i$th pupil in a test on ...
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30 views

How can he assume SD of population equals to SD of sample means?

I'm referring to this KhanAcademy video: https://youtu.be/bekNKJoxYbQ?t=445. My question: How can he approximate the SD of the population to be equal to SD of the sample means? Isn't that SD of the ...
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Simple calculations of mean, standard deviation, and probability

You are a successful entrepreneur that has developed a new sustainable product that is manufactured through a standard production process. As part of this process, the product goes through quality ...
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698 views

Let X = the time between two successive arrivals at the drive-up window of a local bank…

Let $X$ = the time between two successive arrivals at the drive-up window of a local bank. $X$ has an exponential distribution with $\lambda = 2$. That is the probability density of $X$ is $f(X | ...
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161 views

Compute the standard deviation of the monthly cost due to blackouts

Network blackouts occur at an average rate of 5 blackouts per month. Assuming a suitable continuous-time counting process, a. Compute the probability of more than 3 blackouts during a given month. ...
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251 views

Finding the standard deviation without anything except the mean

My statistics professor gave us this question on our last exam and to solve for the standard deviation he just took the square root of the mean, is this correct? Q: An average of 15 aircraft ...
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Weighted Std Deviation of Securities

Corporate Finance problem - can't figure out if I'm right or not but here goes: Probability 15% 35% 20% 30% Security A 8% 5% -4% -6% I need to find mean and std deviation for security A. I got: ...
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37 views

What is var(X / Y)?

I know that: $$ var(XY)=E(X^2Y^2)−E(XY)^2=var(X)var(Y)+var(X)E(Y)^2+var(Y)E(X)^2 $$ But what is $var(X/Y)$? It doesn't seem to be as simple as treating $Y$ above as $1/Y$.
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Standard Deviation. Why do we take the square root of the entire equation?

Please forgive my lack of maths knowledge, It is my understanding that: Standard Deviation is the average distance from the mean in a data set of numbers. Therefore it stands to reason that working ...
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Coffee sales - stats question relating to p-value and test statistics.

I need help mainly with part c of question 11. My work is below. Answer from the back of the book:
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Sample standard deviation and population standard deviation

The average temperature of a particular tropical island is normally distributed with a mean of 74 degrees and a variance of 9 degrees (a) If a random sample of 16 days has been taken, what is the ...
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Statistics: How to compute the probability density distribution of (µ1 / µ2) knowing only µ1, µ2, and standard deviations σ1 and σ2?

Given two means µ1 and µ2, and two respective standard deviations σ1 and σ2 (not variances or standard errors), how can I compute the probability density distribution of µ1/µ2? In my application, µ1 ...
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Combining standard deviations

We have two groups measuring the same resistors, the nominal value is unknown. Group 1 is slower and because of that they did not calcute the s1 empirical standard deviation. Group 1: N1=500 , ...
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find sub-group of any given number [closed]

sorry i couldn't think of better title so i have a number lets say 13(variable) and by dividing it to 5 (constant) i get my groups (3 in this example ) ...
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267 views

Composite variation or standard deviation without common means for more than 2 samples

I know the formula for pooled variance is if the mean for all samples are equivalent and I know that if I want to combine the sigma of two samples with different mu, then the formula is , but what ...
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What is the best distribution that describe the variances $\sigma^2(x)$?

I'm studying a numerical variances $\sigma^2(x)$. For each samples I have more than one hundred of variances. I'm looking for the distribution that can describe them. I think is not Gaussian, because ...
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Find $z$ values for the standard normal variable

Find the following z values for the standard normal variable Z. I got all the answers but B and I am pretty sure I'm right and the answer in the back of the book is wrong.Can you verify? a. P(Z ≤ ...
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Business Statistics problem on my homework

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 84%. What is the risk (standard deviation) that this investment manager has ...
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173 views

Standard deviation of phase for a random phasor sum

I have a phasor sum $a e^{j \theta} = \frac{1}{\sqrt{N}} \sum_{k=1}^{N} \alpha_k e^{j \phi_k }$ where $\phi_k = [-\pi, \pi]$, the standard deviation $\sigma_{\phi}$ of the phase is known and the ...
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Question Regarding finding the mean and variance of a MGF function?

This question confused me at the end where it says a normal random variable. A breakdown of the answer would be great The Question states: The MGF for the (general) normal distribution is given by ...
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Find Standard Deviation Away From the Mean

Word Problem: In one town, the number of pounds of sugar consumed per person per year has a mean of $8$ pounds and a standard deviation of $1.7$ pounds. Henry consumed $11$ pounds of sugar ...
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Use chebyshev inequality to find the probability $P[|X-E[X]| \ge k\sigma]$

 For an arbitrary random variable $X$, use the Chebyshev inequality to show that the probability that $X$ is more than $k$ standard deviations from its expected value $E[X]$ satisfies ...
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Weighted Averages For Grades. But, no score for the final yet. How can I calc?

10% for Participation 10% for Workbooks 10% for Quizzes 40% for Tests 30% for Final Test. Students are asking for their current grade but I thought since one column is blank (final test, not taken) I ...
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What is the probability of two things happening at the same time?

I am using the normal distribution for two events so there is a 34% chance of each event having one standard deviation above the mean. What is the probability of both events having one standard ...
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Standard deviation of the mean through bootstrap resampling of dependent samples

I'm trying to do a Monte Carlo approximation of an integral where the samples are not independent (how much so can be tuned by a parameter giving how often I sample). Therefore the regular expression ...
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Biased estimator for the standard deviation

Question: If a distribution is equally likely to take the values 1 or 4, show that $s_{n-1} $ forms a biased estimator of sigma. I started this question by finding that: $E(X)$ = 2.5, $E(X^2)$ = ...
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Variance is the squared difference - why not to the 3, or 4 instead?

So there is this question about why variance is squared. And the answer seems to be "because we get to do groovy maths when it is squared". Ok, that's cool, I can dig. However, I'm sitting ...
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Definition of Standard Deviation

We note that given a probability distribution function $P$ over a space $U$ the expected value of a function of the elements in U: $$ E(f(x)) = \int_{U} f(x)P(x) $$ We thus consider the mean as the ...
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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 ...