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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Cumulative frequency curve effects on change of standard deviation

Given a cumulative frequency curve . If the standard deviation is lower and median remains the same . Is it true to say that the curve will of the above statement will be steeper and pass through ...
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sum of dependent random variables: [on hold]

Suppose $h=x_1+x_2+..+x_n$ and we have pdf of each $x_i$ (means: $p(x_1 ),p(x_2 ),…,p(x_n )$ )and also $x_{(i )}$ ($i=1,..,n$) are dependent random variables: How can I find the pdf of h?
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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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urgent help needed [on hold]

Question 4 The mean size of commercial loans by a bank has been 60,000 dollars in the past. A recent change in the bank’s credit policy allows larger amounts to be borrowed under the same terms. ...
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Cna someone help me with this [on hold]

Question 3 a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the ...
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If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs.

a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time ...
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The prime minister will accept an error of $5 million in the estimate of µ.

Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. ...
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1answer
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How is the t-statistic computed in this context?

According to pg. 55 of Statistics in Plain English, the t-statistic for the sample mean is $$ t = \frac{\bar{x} - \mu}{s} $$ where $\bar{X}$ is the sample mean, $\mu$ is the population mean, and $s$ ...
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Normal Distribution - What should I study to understand these questions [on hold]

I got these questions from someone. I am not expecting anyone to 'solve' these, just need an idea of which specific topics I should read up on to help the concerned person understand, as I have been ...
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1answer
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Volatility of investment (/w currency hedging)

I´ve been trying to compute a volatility of invesment with currency hedging and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% ...
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21 views

Applications of mean and standard deviation

If I have this set of numbers: [9,7,5,5,4,4,4,2] We know that: mean = 5 variance = 4 standard deviation = 2 But is there an application/formula of standard ...
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How is this not a counter-example to the fact that the standard deviation of a standardized random variable must be 1?

Let $X$ be a random variable that sends all members of the sample space to some constant real number $c$. Let $Z$ be its standardized counter-part. The standard deviation of $X$ is $0$, since $X$ is ...
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The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60.

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60. a) Applicants need a test score higher than 530 to be ...
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Calculating mean and standard deviation of frequency given time displacement data

For example, using this data set (sample rate = 200 Hz): https://my.mixtape.moe/mtyocd.gz If I take the power DFT of it (either unwindowed or with the Blackman-Harris window) and zoom in, I can see ...
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1answer
21 views

How do I find the sample standard deviation given the population standard deviation?

A large population has a mean of 150 and a standard deviation of 40. A sample of 100 observations is to be selected at random from the population. What is the standard deviation of the sample mean? ...
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Create Matrix with Specific Standard Deviation and Mean

Assume I have a matrix $X_1$ which is being generated randomly. For this example we can assume it has 10 rows and 8 columns but the question is general. I want to create a matrix $X_2$ that will ...
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1answer
2k views

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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1answer
885 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
988 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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standard deviation and coefficient of varriation

A sample of 18 employees at a company is monitored to see how long they break for lunch on a particular day. The following data is the lunch break (in minutes) for each worker: ,25 ,25 ,32 ,45 ,22 ,34 ...
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1answer
24 views

Generalised Standard Deviation for less than 50%-50%

I know that for 50%-50% situations like coin toss the standard deviation for N number of toss is given by $$\sigma = \sqrt{.25N} = \sqrt{N}/2$$ What is the type though that I can calculate the ...
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Normal Distribution Problem Normal Graph [closed]

Maple tree diameters in a forest area are normally distributed with a mean of 10 inches and a standard deviation of 2.5 inches. In a forest of 2000 maple trees, how many would have a diameter ...
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Is there a measure of 'evenness' of dispersion?

I looked up on the web, but couldn't find anything helpful. I'm basically looking for a way to measure how 'evenly' a value is distributed. As in, an 'evenly' distributed distribution like X: and ...
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3answers
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Practical intuition for standard deviation

Simply: What is the intuition you get about the data if you are given standard deviation? More detailed: It is easy to imagine some information about the data if you are being told for example mean ...
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variance decreases when x gets farther from the average x?

I just read the description of Studentized residual on wikipeida https://en.wikipedia.org/wiki/Studentized_residual I'm confused about what it says about variace, itt says that "the residuals, unlike ...
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How to calculate mean for standard deviation

I've been doing some standard deviation revision but I'm getting confused as different questions have the mean calculated differently. In some questions, the mean squared is calculated as the actual ...
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deriving mean-variance form

I have a function $$W(x_1,x_2,...,x_n)=A\sum_{i=1}^{n}x_i^2+\sum_{i\ne j}^{n}x_ix_j,$$ where $A \in[0,1)$. And in a paper I am reading, $W$ can be written in the "mean-variance" ...
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calculate the internally studentized residual

This is from my textbook: it says that ...an ordinary residual divided by an estimate of its standard deviation $s(e_{i})$ As we can see from the example that mean for four residuals is 0, so ...
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Z-normalization equation - finding the vector before being applied by Z-normalization

I was trying to find a value $X$ that were used to evaluate $Z$ in this equation $$ Z = \frac{X-\mu_x}{\sigma_x} $$ where $X = \{x_1, x_2,..., x_N\}$ and $Z = \{ y_1, y_2,..., y_N\}$ and $$\sigma_x ...
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How to find n=# of samples

My question is what is the equation to find n if you know standard deviation, and the CI of 95%. Like what is the equation for n?
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1answer
40 views

Calculating the variation coefficient when the arithmetic mean is zero

Introduction I'm just learning statistics so bare with me. I understand that the variance is $\sigma^2 = \frac{1}{n}\sum\limits_{i=1}^n (x_i-\mu)^2 $ and the standard deviation being the square root ...
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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 ...
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Chebyshev Inequality, possible range of 90th percentile of a 100-vector with rms(x)=1

My lecture notes states the Chebyshev inequality as follows: If k is the number of entries of x that satisfy $|x_i − avg(x)| \ge a$, then $k/n \le {(std(x)/a)}^2$. x is a 100-vector with ...
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Interpreting variance and standard deviation in the context of a user interface study

I have been recently carrying out user interface studies. The following graph shows the results to the statement: "I am satisfied with how easy it is to use this mobile application", with each ...
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Standard deviation and alternate measures

Standard deviation is defined by $<(a - <a>)^2>$ for a continuous variable $a$. Does the term $<|a - <a>|>$ contain the exactly the same information. Is there a one-to-one ...
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Adding the averages and standard deviations of different sets correctly

I have $12$ balls with mean weight of $500$g, and S.D $25$g. I have $5$ balls with mean weight $200$g and S.D $10$g. If I combine all of them, is the mean just $8000\over17$ i.e. ...
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Odds to probability - include field size and market dominance

I am trying to understand the conversion of odds to probability. Reading on the internet there seems to be many references to calculations like this. Horse Odds* Probability (from odds) ...
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Method of standardization of essay grades from a number of graders

Basically, there is a group of us grading a few hundred essays. We divided the number up so each of us grade 50, assigning a score 0-100 given a rubric. However, there is still subjectivity in the ...
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Error propagation: add errors in quadrature, or use a weighted standard deviation?

I have a measurement $x$ with a known uncertainty $\sigma_m$. I have a black box that can take an error-free measurement $x$ and produce a value $y$ with a known uncertainty $\sigma_{b}$ (which is ...
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133 views

standard deviation find the probability that more than 30%

A manufacturer produces a certain type of components that has a length of $2.1 \,\mathrm{cm}$. the distribution of this components is normal with mean $2.15 \,\mathrm{cm}$ and sd $0.4 \,\mathrm{cm}$. ...
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Standard error of the estimate

Question: In order to estimate the total weight of rice of 100 bags, a sample of 25 bags was weighted, giving the average weight of 50 kg. If the population standard deviation is 1.5 kg, estimate the ...
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1answer
31 views

Finding the maximum number of students who made a certain score

In a class of 100 students, the mean score of the exam is 75, with a standard deviation of 6. What is the maximum number of students who could have made 100 on the exams? What I tried $P(X = 100) = ...
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Is the variation of the mean 0, and the variance of standard deviation just the variance?

Just trying to get some properties straight. Was looking at a problem online which reads: Let X be a random variable with mean μ and variance σ2. What is the variance of X/σ+10μ? The solution of ...
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Gaussian Smoothing Kernel Sigma from x-axis

I already asked a question and got great swift answers: Gaussian smoothing kernel with different sigma values However I have come across another problem. As I understand it, Gaussian kernels used ...
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1answer
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Normalization of standard deviation

I have a question regarding standard deviation. Let me start with an example: I have response times (RT) from users, let's say RT1 = 3s RT2 = 5s RT3 = 8s I have ...
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1answer
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Explaining the standard deviation formula

I'm revisiting standard deviation for the first time years, and i can't for the life of me recall the difference between two formulas. In particular, im also looking for how we arrived at these ...
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Confirmation of the Variance and Standard Deviation result

The following example is about Variance and Standard Deviation copied from Table 6.1 in the book "The Statistical Analysis of Experimental Data" by J Mandel. The Variance given is 667e-8 and ...
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Standard error of estimate

The question is : In order to estimate the total weight of 100 bags, a sample of 25 bags was weighted, giving the average weight of 50 kg. If the population standard deviation is 1.5 kg, estimate the ...
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How do I calculated a weighted standard deviation for a data set over several years?

I am trying to calculate the standard deviation for the following data set, 2010-2015: 2010: Mean=172.2 StDev=43.2 N=39 WtgMean=29.5 2011: Mean=165.1 StDev=36.9 N=27 WtgMean=19.6 2012: Mean=173.2 ...