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

22
votes
4answers
3k views

Motivation behind standard deviation?

Let's take the numbers 0-10. Their mean is 5, and the individual deviations from 5 are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 And so the average (magnitude of) ...
22
votes
4answers
7k views

incremental computation of standard deviation

How can I compute the standard deviation in an incremental way (using the new value and the last computed mean and/or std deviation) ? for the non incremental way, I just do something like: ...
14
votes
1answer
52k views

Sample Standard Deviation vs. Population Standard Deviation

I have an HP 50g graphing calculator and I am using it to calculate the standard deviation of some data. In the statistics calculation there is a type which can have two values: Sample Population I ...
13
votes
5answers
693 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 ...
12
votes
2answers
46k views

Determining variance from sum of two random correlated variables

I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated? ...
7
votes
3answers
516 views

Variance of a max function

Say $x_1$ and $x_2$ are normal random variables with known means and standard deviations and $C$ is a constant. If $y = \max(x_1,x_2,C)$, what is $\mathrm{Var}(y)$? Well, I forgot to tell that $x_1$ ...
6
votes
4answers
3k views

How can I calculate “most popular” more accurately?

I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ...
6
votes
4answers
303 views

Why do statisticians like “$n-1$” instead of “$n$”?

Does anyone have an intuitive explanation (no formulas, just words! :D) about the "$n-1$" instead of "$n$" in the unbiased variance estimator $$S_n^2 = \dfrac{\sum\limits_{i = 1}^n ...
6
votes
0answers
39 views

Relationship between exterior power of representation and variance?

I was reading the question: Symmetric and exterior power of representation regarding how to determine the character of an exterior power of a representation from the original representation. One of ...
5
votes
1answer
458 views

Standard Deviation. Why do we take the square root of the entire equation?

Please forgive my lack of maths knowledge, It is my understanding that: Standard Deviation is the average distance from the mean in a data set of numbers. Therefore it stands to reason that working ...
5
votes
1answer
48k views

How to determine if Standard Deviation is high/low

I have derived the following response time data for a performance test I am running: Min - 8sec Max - 284sec Average - 28sec Standard Deviation - 27sec What does the standard deviation say about the ...
5
votes
1answer
1k views

Standard Deviation: Why divide by $(N-1)$ rather than $N$?

The forumlae for standard deviation seems to be the square root of the sum of the squared deviation from mean divided by $N-1$. Why isn't it simply the square root of the mean of the squared ...
4
votes
3answers
163 views

How are the following two Chebychev's inequalities equivalent?

I was looking at the following definition of Chebyshev's inequality $$P(|X - E(X)| \geq r) \leq \frac{Var(X)}{r^2}$$ which includes the expected value and variance of $X$, and then I discovered ...
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 ...
4
votes
1answer
1k views

Denominator to calculate standard deviation

I've just read something about calculating sample standard deviation. Some explanations say that it is because of degree of freedom. With a constraint that the mean should be zero, we do actually have ...
4
votes
1answer
1k views

Standard deviation calculation not matching up

I was looking up how standard deviations work, and tried to do it by hand, but what I'm getting isn't matching up with what I have in SQL Server. My population is: 1,2,3,4,5,6,7,8,9. I end up with ...
4
votes
1answer
499 views

Generate a set of random numbers with a normal distribution

I am trying to generate a set of N random numbers where the set has a normal distribution. I'm currently using a brute force approach: Randomly select N numbers from a normal distribution. Check ...
4
votes
1answer
66 views

Bootstrap method failing where blocking works

I'm computing an average of individual samples that are not entirely independent and need an estimate for the true standard deviation. According to Newman and Barkema's book the most reliable method ...
4
votes
3answers
11k views

Standard deviation of the weighted mean [duplicate]

How do you find the standard deviation of the weighted mean? The weighted mean is defined: $\bar{x}_w = \frac{\sum{wx}}{\sum{w}}$ The weighted standard deviation (since it is not specified, I take ...
3
votes
4answers
4k views

Why is there not a simpler way to calculate the standard deviation?

Steps of getting standard deviation. http://www.techbookreport.com/tutorials/stddev-30-secs.html: Work out the average (mean value) of your set of numbers Work out the difference between each ...
3
votes
3answers
1k views

Is Standard Deviation the same as Entropy?

We know that standard deviation (SD) represents the level of dispersion of a distribution. Thus a distribution with only one value (e.g., 1,1,1,1) has SD equals to zero. Similarly, such a distribution ...
3
votes
2answers
7k views

Is it possible to calculate the mean and standard deviation from a median and quartiles?

Any advice would helpful. I understand that the reporting of median and quartiles for small samples is an indication of skewed data. If such is correct, then is it useless to try to work out the mean ...
3
votes
2answers
66 views

Calculating the sample standard deviation

I've been preparing for an exam tomorrow and was doing a past paper when it appears the mark scheme has an answer that I just cannot fathom. The exact question is to "find a 95% confidence interval ...
3
votes
3answers
2k views

7.7 standard deviations away from the mean?

I'm confused. I have a problem where I have to find the probability that x is below the z value 7.7. My z table only goes to z values of 3.4. How do I calculate this? These are the hints my teacher ...
3
votes
1answer
21k views

What is difference between standard deviation and Z-score?

I have read several explanations of standard deviation and z-score, I know how to it calculate them but I am not sure what is differences betwen them. Can someone explain it to me? When is suitable ...
3
votes
1answer
6k views

Prove one standard deviation lies on inflection points

Is my conjecture correct that one standard deviation lies on the inflection points of the normal distribution curve (of the probability density function)? How can it be proved using the standard ...
3
votes
1answer
6k views

How to calculate the expected value $E(XY)$ with known $E(X)$, $E(Y)$ and $\sigma_{i}$?

I am trying to understand the value of $\bar{x_{1} x_{2}}+E(x_{1} x_{2})$. For all $i$, $E(x_{i})$ and $\sigma_{i}$ are given. Wikipedia gives the joint probability density function: $E(XY) = \int ...
3
votes
5answers
201 views

Why the natural log is there in MLE?

Why do we use natural log for MLE?
3
votes
1answer
3k views

Is standard deviation additive?

I am helping someone study for a statistics exam. I am quite good at most other math classes but it's been a while since I studied statistics. I am stuck on one of the exercise problems that we worked ...
3
votes
1answer
109 views

Estimate the sample deviation in one pass

We've learned this algorithm in class but I'm not sure I've fully understood the correctness of this approach. It is known as Welford's algorithm for the sum of squares, as described in: Welford, ...
3
votes
1answer
7k views

How can I calculate the standard deviation knowing an event probability and a number of trials?

I'm writing a test for a probabilistic data structure that I've implemented. Since its probabilistic, its performance is different every time, and in particular, the performance varies much more ...
3
votes
1answer
186 views

Help with understanding point from Nassim Taleb's book “Dynamic Hedging”

This is an excerpt from Nassim Taleb's book "Dynamic Hedging" (a book on option trading strategies) page vii Most examples in this book are presented as generic situations. The volatility will ...
3
votes
1answer
319 views

Question about an article by Nassim Nicholas Taleb about the problems with standard deviation.

The article by Nassim Nicholas Taleb says that using standard deviation is flawed and is poorly understood and mean absolute deviation should be used. Because this article is short, and I don't ...
3
votes
1answer
2k views

Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
3
votes
2answers
23k views

How to interpret standard deviation of samples with different means?

Let be two samples collections A and B. Mean of the first is 5 and the second is 15. Standard deviation of the first is 2 and the second is 5. Can we conclude something even though the two datasets ...
3
votes
1answer
58 views

AWG Noise and RMS Voltage

A question says, a channel is corrupted by Additive White Gaussian Noise with zero mean and RMS voltage 20 nV. The probability that the noise voltage is less than a particular positive value c is 0.9. ...
3
votes
1answer
661 views

Standard deviation: mathematical manipulation

I am learning about standard deviation. In the book I am reading it defines standard deviation as: $$\sigma^2 = E[(x - E[x])^2]$$ so far no problem. In then states "simple mathematical manipulation ...
3
votes
1answer
573 views

Finding probability 400 components last 5012 or less hours using standard deviation?

The lifetime of certain electronic components is a random variable with the expectation of 5000 hours and a standard deviation of 100 hours. What is the probability that the average lifetime of 400 ...
3
votes
2answers
318 views

Course Grade - Statistics Question

I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows: ...
3
votes
1answer
45 views

Correct Intuition? Standard Deviation and distance in $n$ dimensional space.

Basic Question Is there an intuitive explanation of standard deviation in terms of Euclidean distance in $n$ dimensional space? Longer Version of Question To begin a more detailed sketch of my ...
3
votes
1answer
66 views

What is the maximum value of the sum $\sum_{i=1}^L(\bar{x}-x_i)$, in this specific case.

Let $x_i$ be a positive real variable, with $i=1,2,...,K$. We denote by $\bar{x}$ the average value of the values $x_1, x_2,...,x_K$. Let $a=\min_i x_i$ and $b=\max_i x_i$, then $x_i \in [a,b]$. My ...
3
votes
1answer
60 views

95% Confidence Intervals

I was solving this problem from a textbook In a random sample of three pupils, $x_i$ is the mark of the $i$th pupil in a test on volcanoes and $y_i$ is the mark of the $i$th pupil in a test on ...
3
votes
1answer
404 views

fantasy basketball model

i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team ...
3
votes
1answer
81 views

Standard Deviation of a Magic Square

I'm not sure if this is the right stackexchange to post this question to, but I was just wondering if someone had the answer to an interesting observation I've made. I've written a program that ...
3
votes
3answers
795 views

How to calculate the standard deviation of numbers with standard deviations?

I have essentially a propagation-of-error problem I run into frequently with my scientific data. For example, I have three samples, each of which I take two measurements of. So, for each sample, I can ...
3
votes
1answer
114 views

Mean or standard deviation?

Which one of mean or standard deviation can used to solve the following problem? A light bulb is considered defective if it lasts less than 400 hours. The following claim is made: 'Brand A ...
3
votes
1answer
147 views

Standard error and p-values

I am a scientist who is currently doing a BSc. I did some stats a few years ago but since haven't touched it. I'm not sure how to calculate p-values for my data. A bit of background is that I am ...
3
votes
1answer
215 views

Max of multistep Gaussian walk vs max of multiple single-step Gaussian walks

Is there a relation between the max of a Gaussian random walk of 10 steps vs the max of 10 Gaussian random walks? Specifics (in Mathematica notation): ...
3
votes
1answer
48 views

How many points necessary for standard deviation?

First off, I'm not a mathematician, and never took statistics in college, what I know about standard deviation I've learned in the past few weeks, so be gentle... I'm working on a piece of software ...
3
votes
0answers
28 views

Removing slope from running times

First of all, & looking at the suggested question list, I hesitate at asking this basic question: Here goes. I'm trying to assess my fitness, and I need a bit of mathematical help. I do a little ...