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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Binomial theorem estimate for very large samples

I have around $2^{105}$ balls, of which 1 in 20 is white. I expect that when I draw a random sampling of them, roughly 5% of all balls drawn would be white. What is the probability that, if I draw ...
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Find the Average Score Given the Standard Deviation

I think I'm supposed to use $z = (X - \bar X)/S$ but I'm not sure how to apply it properly to this problem. Kyle got an 8.25 on his previous test while the average score was a 7.2 and the ...
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According to Chebyshev's rule, how many observations should lie within one and a half standard deviations of the mean?

Using the formula : $p = 1 - k^{-2}$ I calculated that $p = 1 - 1.5^{-2} = 0.56$ , which equals to $56\%$. Because I have $24$ data points I go ahead and solve the number of points is $56\%$ of ...
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sample standard deviation given population standard deviation

How do you find the sample standard deviation when given the population standard deviation? What formula do you use? If you can make up an example that would be great.
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Sample standard deviation from population standard deviation [closed]

How do you find the sample standard deviation when given the population standard deviation and no other data? What formula do you use?
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Calculate popularity (frequency) of an item sold from multidimensional array [closed]

I have an array extracted from my database online where i store id status: sold / not sold time: day that the item sold or not price sold and the output example is given below ...
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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
36 views

How to find the standard deviation from the given information and what is $B(0)$ equal to?

Assume that the risk free rate is $0$ and that the stock price is given by the equation $S(t)=6e^{2t+2B(t)}$ where $B(t)$ is the standard Brownian motion. Determine the price at time $0$ of the ...
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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
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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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1answer
399 views

How do I calculate a point estimate of the largest 10%?

Here is the provided data: The question asked is: Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90% and state ...
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Proof that there will always be data within 1 SD

So we just started stats at school, and our teacher told us that no matter the data, no matter how distorted or weird it is, there will always be data within 1 standard deviation of the mean. Is this ...
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31 views

Understanding the value of standard deviation

I have two datasets $\{10,10,2,2\}$ and $\{13,7,0,4\}$. Now, when I compute standard deviation for both the sets, I get $4$ and $4.74$ respectively. My question: what is the significance of $4.74$ or ...
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Questions about Ridge Regression, how to explain the penalty term?

I have read the introduction of ridge regression in https://tamino.wordpress.com/2011/02/12/ridge-regression/. As we know, the equation of OLS is ∥ y − X β ...
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How does using one distribution as another's sample size affect variance?

How does using one distribution as another's sample size affect variance? For example, let's say I roll a 6-sided dice and record the number shown. Then, I roll 'that many' 6 sided dice more and ...
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1answer
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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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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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1answer
553 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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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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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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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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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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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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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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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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1answer
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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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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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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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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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1answer
23 views

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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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 ...