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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mean time question [on hold]

A sample of 600 units yields a mean of 7.2 days.since the population standard deviation of s=1.9 days must be used. Calculate & interpret the 90 percent interval for the mean completion time for ...
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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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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
22 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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1answer
28 views

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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20 views

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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1answer
161 views

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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21 views

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
9 views

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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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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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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24 views

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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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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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
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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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12 views

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
22 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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31 views

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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1answer
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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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1answer
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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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
21 views

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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1answer
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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 ...
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1answer
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Given mean and standard deviation of the number of accidents in Town A, find mean and variance in Town B.

I'm having some trouble figuring out this question: The number of car accidents in Town A has mean $2.3$ car accidents per hour with standard deviation of $1.5$ car accidents per hour. It is ...
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1answer
41 views

Find probability that a newborn weighs between $6$ and $8$ pounds; given mean and standard deviation but not given sample size

The weight of a newborn baby randomly sampled from a particular population of babies is known to be normally distributed with a population mean weight of $7.25$ pounds and a population standard ...
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How to calculate sample variance?

I have an infinite population. Out of this population, I'm picking $N=40$ items, each of which can have a value of $0$ or $1$. Say I get a mean of $0.7$. How do I calculate the standard error of this ...
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error on the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as ...
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21 views

Recalculate Standard Deviation

I know how to calculate a standard deviation when given a set of values. You must calculate the mean, then square the difference of each value between the mean to get the variance. Lastly, the ...
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2answers
47 views

Root mean square distance explanation

We know that $D_{rms}=\sqrt N$ where $N$ is the number of steps taken by the random walker. Now,consider a situation where a random walker walks $2$ steps in positive direction in the first two ...