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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Analyze mean in difference in before and after measurements

I am trying to decide the best way to measure the realationship in the difference between the before and after measurements of a single group. So say I measure the weights of a group 6 subjects(A-F): ...
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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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24 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
19 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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1answer
31 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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Normal Distribution Question [on hold]

The time (in minutes) taken by a group of students to complete a maths test is normally distributed with mean of 60 and a standard deviation of σ. If 34% of these students took between 51.2 and 68.8 ...
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1answer
18 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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42 views

Standard deviation and mean question [closed]

The pulse rates of healthy adults are normally distributed with mean 72 and standard deviation of 5. i) Approximately ninety-five percent of the adult population can be said to have their ...
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23 views

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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10 views

What are the bounds on Variance?

I have an image which can be considered as a 2D plane. Now, I have to check the variance of some points which are distributed over this 2D plane. TASK: I want to calculate the variance to predict if ...
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3answers
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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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19 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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1answer
23 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
23 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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1answer
47 views

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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1answer
19 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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1answer
71 views

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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1answer
69 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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1answer
39 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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1answer
27 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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28 views

Standard Deviation divided by Mean

I am comparing different lists of numbers to find the one which "varies least", in a common sense of meaning. Because the lists differ greatly in their mean value (some are around 0.3, others are ...
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11 views

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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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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1answer
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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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1answer
44 views

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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21 views

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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26 views

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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11 views

Function For Calculating Average Excluding Outliers

I'm looking for a function that will let me take an average and exclude outliers. Basically something where: 1, 2, 1, 2, 7 Would average out to 1.5. Would that be along the lines of standard ...
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1answer
26 views

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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1answer
13 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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2answers
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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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1answer
80 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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1answer
15 views

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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19 views

Is Residual Standard Error the same as Residual Standard Deviation?

R's output gives you the Residual Standard Error but I am asked for the Residual Standard Deviation. Are those numbers the same? Also, how would you interpret the residual standard deviation? Thanks
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1answer
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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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Probability and Standard Deviation Study Help

I am studying for a mid term that I have tomorrow with last years exam. I went through it and did as much as I could. These are the two questions I didn't get correct. The correct answers (given) are ...
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Math Expectations and Standard Deviations

Pizza Shop profits are $1, $3, and $2 for each sale of their small, medium and large pizzas, respectively. If these are the probability distributions Small Size: $1 - 0.40 Medium Size: $3 - 0.20 ...
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calculating a moving average rate for detecting an outbreak

I have a count for the number of occurences of a disease over a period of time. I want to set a threshold for detecting unusaul increase with a moving average. I am planning to use + 1,2,3 SD to set ...
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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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Error from bias and noise in a linear operator

There's a result $S$ that depends linearly on some forcing $F$: $S=\int dt' G(t-t')F(t')$ Let's say I need to predict $S$, but can't measure $F$ exactly. I have both bias and noise in my ...
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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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3answers
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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 ...