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
0answers
13 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 ...
0
votes
2answers
41 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 ...
1
vote
1answer
23 views

what is the unit of the following standardization formula?

If normalization would be to rescale the range of values to scale between $0$ and $1$ as follow: $x^{'}=\frac{x-\min(x)}{\max(x)-\min(x)}$ where the interval of $x^{'}$ is closed between $[0,1]$ ...
0
votes
1answer
19 views

Mean and standard deviation after a coin is tossed

Could someone help solve this? Let X equal the number of heads when $3600$ coins are tossed. Find the Mean and Standard Deviation of X
0
votes
1answer
19 views

Does a larger coefficient of variation mean larger variability?

I'm reviewing right now for an exam and I've stumbled across this online reviewer. In the solution for question #2 it stated that Section B is more consistent so there is greater variability in the ...
0
votes
1answer
30 views

How do you calculate the correlation between the intercept's and beta's standard error in a univariate linear regression?

I am running a regression to predict a variable Y as follows: $Y=\alpha+\beta\times x+\epsilon$ I am trying to get a distribution of the expected value of Y given standard errors in the model ...
1
vote
0answers
18 views

Removing outliers from a dataset [migrated]

Assume I have a big dataset (million numbers), and I want the smallest range without outliers. So e.g. I have: $$x=[1,1,50,50,50,50,50,50,50,50,51,51,51,51,10000,10000]$$ I am looking for "the ...
0
votes
1answer
19 views

Standard deviation and standard error

I have a homework in which I am using data from NFL teams. This information was taken from the ESPN site and I was asked to calculate the following: $mean$, $standard$ $deviation$ and $standard$ ...
0
votes
0answers
14 views

SD probability problem involving chi-square distribution

Preparing for an exam in statistics, I have been pondering the following problem: Given that in country X 14 % of people hold a university degree, find the probability that for random sample of size ...
1
vote
0answers
44 views

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 ...
0
votes
0answers
17 views

Standard deviation and statistics

The concentration by volume of air mixing with methane is distributed with a mean of 20% and a standard deviation of 7%. I want to find the probability that the concentration is less than 30% or ...
0
votes
1answer
22 views

Calculating the standard deviation involving a moment generating function

An actuary determines that the claim size for a certain class of accidents is a random variable, X, with moment generation function: $$M_X(t)=\frac{1}{(1-2500t)^4}.$$ Calculate the standard deviation ...
0
votes
1answer
34 views

What do I plug in for the z score?

Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However since the filling machine is not always precise, there can be variation from bottle to bottle. The ...
0
votes
2answers
28 views

How do I find the $Z$ value and calculate the $P$?

Please DO NOT answer the question, as I just need the right formulas in the form of plugging the numbers from the word problem into it. I struggle with this. And I need to find what the percentage is ...
0
votes
1answer
22 views

Ratios of median/mean and standard deviation/IQR in a normal distribution

I have some queries on the following question For a normal distribution, find the ratios of: (a) $\frac {\mbox{median}}{\mbox{mean}}$ (b) $\frac {\mbox{standard deviation}}{\mbox{interquartile ...
0
votes
1answer
22 views

Normal Distribution, percent less than mean minus one std. dev

GRE Question, part b. My answer is 16%, but the book says 15%. Why? mean = 65 cm stdev = 5 cm Probability that penguin chosen at random will be less than 60 cm is 16%, it shows in Normal ...
0
votes
1answer
46 views

Determine the standard deviation for statistical hypothesis testing when not explicitly given

I have got a video in grayscale, and I am interested to find out if the intensity of a pixel at a given location is more or less constant over time. I have been told here that I can use linear ...
4
votes
2answers
71 views

Standard Deviation vs Population Standard Deviation

In GRE study guide, it gives difference between standard deviation and sample or population standard deviation. I understand the mechanics of this, i.e. in standard deviation you divide all ...
1
vote
1answer
21 views

Normalize a list of standard deviations

I have several columns of features that I need to normalize to values between 0 and 1 (or -1 and 1, etc.--just something standard) in order to do regressions using ML algorithms (such as SVR, KNN, ...
1
vote
2answers
92 views

Is it valid to calculate standard deviation for n=2?

My colleagues and I are having discussion whether it's valid to calculate standard deviation for $n=2$ or not? I think it's valid since I can calculate based on the equation, but higher N will give ...
0
votes
0answers
31 views

Standard deviation problem for short cut technique

Revised-GRE QUESTION I know how to evaluate the standard deviation and mean and also I have basic knowledge about the bell curve. But whenever I have to solve some problems related standard ...
0
votes
1answer
12 views

Mean of the deviations from the mean

I ve been struggling to understand the below problem.If I could get help with this problem, it would be greatly appreciated. Consider the data y, y+a, y+2a,….,y+na and the deviations of these ...
1
vote
1answer
11 views

Standard deviation without square

For $(x_i)_{1 \leq i \leq N}$, the standard deviation is of course $$\sigma = \sqrt{\frac{1}{N} \sum_i (x_i - m)^2},$$ where $m$ is the mean value of the $(x_i)$. We can say that the variance ...
13
votes
5answers
696 views

How can the standard deviation be interpreted when the range is partially impossible?

After meassuring the answer time of a software system I calculated the standard deviation from the samples. The average time is about 200ms, the standard deviation $$\sigma = 300ms$$ According to the ...
0
votes
1answer
10 views

Using Minitab to compute an upper confidence bound for std deviation.

I've got a set of data and I want to answer the following: ...
0
votes
0answers
21 views

Specific confidence intervals question

As of now, I completely suck at computing confidence intervals, and I have an exam in a couple of days. The exact question is as follows: Some people are trying to measure a certain parameter ...
1
vote
1answer
48 views

Why the standard deviation of the sample mean is calculated as $\frac{\sigma}{\sqrt{n}}$?

According to Wikipedia, the standard deviation of a sample mean is calculated as follows $$\frac{\sigma}{\sqrt{n}}$$ Why is that? Why do we need to divide the standard deviation of the population by ...
1
vote
3answers
36 views

Formula for standard deviation

So I am studying for a final exam and I know, or thought I knew, the formula for standard deviation. I quadruple checked in my notes and the slides for the lecture and see that the formula for the ...
0
votes
0answers
12 views

Did I equate the standard deviation correctly?

This was for a frequency table, so I will start from finding the mid points. For standard deviation, find the squares of the midpoints then multiply them by the frequency 7500.5², 12500.5², 17500.5², ...
0
votes
1answer
38 views

Is there a lower bound to the standard deviation of a Gaussian (Normal) distribution?

A Gaussian or Normal distribution is defined by the probability density function $$ f(x \; | \; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} } $$ with $\sigma$ as ...
0
votes
0answers
33 views

Standard Loss Function L(z)

z is the standard normal distribution F(z) is the probability normal distribution L(z) is the standard loss function i can find these values using below code in the excel z=NORMSINV(x) ...
0
votes
0answers
8 views

Finding the variance of a group data set

Okay, so this is what I have so far for the means of these numbers. At this point I've added so many numbers together that my calculations are getting messed up. I need to know how to find the ...
0
votes
0answers
8 views

How do I find the variance for a group data set?

Okay, so this is what I have so far for the means of these numbers. At this point I've added so many numbers together that my calculations are getting messed up. I need to know how to find the ...
0
votes
0answers
41 views

A jar contains seven red and three green beans.

Four beans are randomly withdrawn in succession with replacement, and the number of red beans, $X$, is observed. Determine $\mu$, $\sigma_2$, and $\sigma$ for the random variable $X$. I'm not ...
0
votes
1answer
10 views

How do I find the variance for a range of numbers?

Basically, my homework is asking me to find the variance based on a frequency table. But the frequency table looks like this: Frequency Table: Salary Number of Employees 5,001–10,000 8 employees ...
0
votes
0answers
11 views

How do I find the variance for a range of salaries?

For instance, if I am looking at a frequency table and it says that 6 employees make between 5k-10k, 5 employees make 12k-18k, and 3 employees make 20k-25k...how would I find the variance if the ...
1
vote
0answers
60 views

Am I on the right track with this question on standard deviation?

The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean? ...
0
votes
0answers
14 views

Question about checking normal distribution and analysing confidence intervals

I've got another question about normal distribution and its confidence intervals interpretation. Your explanation will respectively help me to better prepare for my examination. One of the social ...
1
vote
1answer
23 views

Two questions about normal distribution and its calculation

dear community members, I got this question in my handbook for exam preparation. I was trying to calculate the output but I'm stuck with figuring out the correct value. The question is: According to ...
0
votes
0answers
33 views

Was it really necessary to have the variance be calculated with $\Sigma (X-\mu)^2 $? [duplicate]

From what I understand, in calculating $$\sigma^2 = \frac{\sum (X - \mu)^2}{N}$$ the only reason why the squaring is done is to make distance from mean always positive. So my question, why couldn't ...
0
votes
0answers
17 views

OLS on big data

We regress $Y$ on categorical data $X_1,…,X_p$. This is a large data set (that's right, big data!) but many of the rows of the design matrix are duplicated. We can summarize the data by averaging $Y$ ...
0
votes
1answer
46 views

Normal Distribution and Percentile Word Problem

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with mean ...
0
votes
1answer
47 views

Aggregating standard deviation to a summary point

I have a range of data (server performance statistics) is formatted as follows, for each server: ...
0
votes
1answer
21 views

Variance of Normal Distribution

Consider $X_1$~normal(4,3) , $X_2$~normal(5,7), and $X_3$~normal(6,4), where $X_1$, $X_2$, and $X_3$ are independent. Obtain variance of $W = 2X_1 - X_2 + 3X_3 + 3.$ Attempt : Since we are ...
0
votes
1answer
35 views

Chebyshev inequality for standard deviation

everyone! I have a question when I studied matrices of norm and distance. Chebyshev inequality for standard deviation. If $k$ is the number of entries of $x$ that satisfy $$ |x_i - ...
0
votes
0answers
14 views

Standard deviations assume a white noise component

"The important point is that these standard deviations assume a white noise stochastic component which will rarely be true for time series." Why do these standard deviations assume a white noise ...
1
vote
0answers
32 views

What is the difference between root mean square, and standard deviation?

I am currently working through the Feynman Lectures, chapter 6: Probability. I have reached his problem of the "random walk". After deriving this and getting some root mean square, wouldn't this ...
0
votes
1answer
14 views

Is Standard Deviation Independent of Sample values

I have a rule to implement which says that if standard deviation of a set of measurements is > x, then y is true. Problem is that my values could be anything like: 1,1.1,1.2,1.2,1.3.. or 100, ...
2
votes
0answers
47 views

Understanding the Normal Distribution?

If a sample is normal with observations independent and identically distributed: $\mu|\sigma^2 \propto N(\beta \,,\,\sigma^2/\, n_0)$ How can I show that $\mu\,|\,x_1,x_2,....x_n\,,\,\sigma^2 \sim ...
0
votes
0answers
18 views

Can variance be greater than mean and samples?

Assume I have some samples 91.7526, 79.0083, 64.9485, 52.8719, 88.4585. Calculated variance is 266.9257. Can variance be greater than sample value and mean?