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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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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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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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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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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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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605 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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323 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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3answers
169 views

How to calculate the standard deviation of numbers with standard deviations?

I have essentially a propagation-of-error problem I run into frequently with my scientific data. For example, I have three samples, each of which I take two measurements of. So, for each sample, I can ...
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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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1answer
389 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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1answer
874 views

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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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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3answers
25 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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18 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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2answers
400 views

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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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
620 views

Converting standard deviation number

This is math finance question. I'm trying to figure out the formula for converting the standard deviation of % changes in prices for a sample of days into the standard deviation of % changes in prices ...
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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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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
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
38 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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1answer
330 views

What does the multiplication of standard deviation of two variables gives?

If we need to find the correlation between two variables it is given by the formula - co variance of two variables divided by the multiplication of Standard deviation of the two variables. My ...
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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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27 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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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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301 views

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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424 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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1answer
43 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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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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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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300 views

Stuck…please help to understand how formula works in order to Find the standard deviation in normal distributions

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 81%. What is the risk (standard deviation) that this investment manager has ...
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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 ...
2
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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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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 ...
0
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2answers
32 views

SD from Mean and Median

Given the mean and median of a dataset, is it possible to compute the standard deviation of the dataset?
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Financial Calculator HP 10bII - Standard Deviation with Probability

I have a financial calculator and am trying to use it to calculate the standard deviation when probability is involved. For a standard deviation question say on the numbers $1$, $5$, $6$, $10$ ...
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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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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 ...