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.

learn more… | top users | synonyms

0
votes
1answer
19 views

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 ...
0
votes
0answers
7 views

Why %RSD of execution times, while sorting hundreds of arrays, is lower for larger arrays of random integers?

I am experimenting with the sorting of arrays and their execution times. While using bubblesort, insertsort and ...
0
votes
1answer
25 views

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 ...
0
votes
1answer
30 views

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.
-3
votes
0answers
20 views

Sample standard deviation from population standard deviation [on hold]

How do you find the sample standard deviation when given the population standard deviation and no other data? What formula do you use?
0
votes
0answers
7 views

Calculate popularity (frequency) of an item sold from multidimensional array [on hold]

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 ...
0
votes
1answer
35 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 ...
0
votes
1answer
27 views

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 ...
0
votes
1answer
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 ...
0
votes
0answers
19 views

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 ...
1
vote
3answers
44 views

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 ...
0
votes
0answers
3 views

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 ...
0
votes
0answers
40 views

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 ...
0
votes
0answers
17 views

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. ...
0
votes
1answer
22 views

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 $s$ ...
0
votes
1answer
24 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 ...
1
vote
1answer
30 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% ...
0
votes
0answers
21 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 ...
0
votes
1answer
173 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 ...
0
votes
0answers
9 views

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 ...
1
vote
1answer
25 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? ...
0
votes
0answers
23 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 ...
-2
votes
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 ...
0
votes
1answer
26 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 ...
-1
votes
1answer
24 views

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 ...
0
votes
0answers
11 views

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 ...
0
votes
0answers
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 ...
1
vote
3answers
43 views

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 ...
1
vote
0answers
33 views

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" ...
1
vote
1answer
17 views

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 ...
0
votes
0answers
3 views

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 ...
0
votes
1answer
14 views

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?
1
vote
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 ...
1
vote
0answers
16 views

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 ...
0
votes
0answers
10 views

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 ...
0
votes
0answers
13 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 ...
1
vote
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. ...
1
vote
1answer
34 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) ...
2
votes
1answer
25 views

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 ...
0
votes
0answers
15 views

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 ...
1
vote
1answer
137 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 $0.4 \,\mathrm{cm}$. ...
1
vote
0answers
13 views

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 ...
1
vote
1answer
32 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) = ...
0
votes
0answers
6 views

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 ...
0
votes
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 ...
2
votes
1answer
40 views

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 ...
0
votes
1answer
11 views

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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
14 views

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 ...