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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Standard deviation on absolute square of complex average

I am calculating a quantity $q=|c|^2$ where I obtain $c\in\boldsymbol C$ as an average of a collection of estimates with errors: $\langle c\rangle=\sum_{j=1}^nc_j$, and the question is what error to ...
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Conclusions to be drawn from mean, median, stdev, and range

From a sample of size n = 100, the following descriptive measures were calculated: median=23, mean=20, standard deviation=5, range=35; 75 sample values are between 10 and 30; and 99 sample values are ...
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Taking the standard deviation over multiple assignments?

Lets say that a group of students all take 5 tests, with the average and standard deviations as follows: test 1: mean 43/50, SD 8 test 2: mean 23/30, SD 4 test 3: mean 56/70, SD 12 test 4: mean ...
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Probability and Standard Deviation

Hey I'm confused about how to do this kind of problem. I can't figure out how to find the standard deviation. There are on average 4 tetanus cases reported in the US each month. What is the ...
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2answers
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how to find standard deviation when given a percentage?

I'm stuck on this question, can anyone help? An electronics company's biggest seller is a talking toy. Of the toys produced, 4% have a defective voicebox. A quality control tech randomly collects 250 ...
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“Reverse” distribution-tails

Chernoff, Markov and Chebyhev all give some upper bound for tail probabilities, e.g. Chebyshev gives us $Pr[|X-E[X]| \geq t] \leq \frac{Var[X]}{t^2}$. This is quite helpful, but what if I would ...
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Mean and variance: Gaussian is the most conservative assumption

"given only the mean and variance of a distribution, the most conservative assumption that can be made about the distribution is that it is a Gaussian having the given mean and variance" I've read ...
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stdev and mean from gaussian fit vs. from classical formula

I have a set of data - measured speed of molecules in water. I made a histogram and fitted it with function $$A\exp\frac{(x-B)^2}{C}$$ calculating mean and standard deviation from values B and C If I ...
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problem on standard error in sample data

From a population of 20,000 observations, a sample of 500 observations is selected. how to Calculate the standard error of sample mean if the population standard deviation equals 20.
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2answers
21 views

Problem on Standard Deviation

A man has observed the number of chocolates eaten by his son for 32 days.The total number of chocolates eaten by his son is 80 and the sum of the squares of the chocolates eaten everyday is 1000, then ...
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Confidence intervals and dividing by $n^{0.5}$

I am studying a-level and am confused when I divide the standard deviation by $n^{0.5}$ when doing confidence intervals. To put it another way when I don't divide by it? (where $n$ is the number of ...
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Identification of linear regression function under $\ell_1$-norm criterion.

Consider a linear system \begin{align*} y = \theta^Tx + e, \end{align*} where $x\in\mathbb{R}^n$ and $e\in\mathbb{R}$ are independent Gaussian random variables with distribution $\mathcal{N}(0,I_n)$ ...
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1answer
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Standard Deviation and Mean

take a look at this question: The sample from Population A has a mean of 35 and a standard deviation of 1. The sample from Population B has a mean of 45 and a standard deviation of 15. Which of ...
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1answer
32 views

Confidence interval for n=1, unknown standard deviation

Is there any way to calculate a confidence interval (or otherwise gauge the reliability of a sample) when you have a sample size of one and you don't know the population standard deviation? I work at ...
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1answer
29 views

What is the corrected sample standard deviation when there is only one sample?

What do we say about the corrected sample standard deviation when the sample size is one? Do we just assume it is 0? Is it even meaningful? The usual equation seems to fall apart here because N - 1 ...
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Establishing the upper and lower bounds of normal using standard deviation

I understand the concept of standard deviations and z-values, but I'm trying to figure out if standard deviations alone are good for establishing the upper and lower bounds for normal. For example, if ...
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2answers
28 views

Normal Distribution Problem

The time taken for a computer to connect to a server is normally distributed with a mean value given by 3.3 seconds and a standard deviation of 0.66 seconds. (a) A computer is said to have a fast ...
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1answer
32 views

Percentage with only standard deviation and mean given. [closed]

I have some questions that I really need help with. The mean mark for an IQ test in the population is 100, with a standard deviation of 16.5. The IQ is normally distributed. Your IQ is 113. a. ...
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1answer
13 views

How to calculate standard deviation from mean and probability?

What's the formula to calculate the standard deviation knowing the mean and a certain probability, but not knowing all the n's. http://stattrek.com/online-calculator/normal.aspx For example, ^that ...
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41 views

Probabilities and Estimation of average and standard deviation

I've done a good bit of this number but I have trouble with part 2. I'll show you my work and the questions I can't figure in bold. A guy has a machine that scans his apples. The machine rules are : ...
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Is it possible to convert calculate the percentile and t-scores from mean and standard deviation?

I need to produce a table that will allow you to look up various types of scores for a test using the number of correct answers like this: ...
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1answer
25 views

Fast way to recalculate average and standard deviation as new values arrive

Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...
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1answer
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hypothesis testing two sample problem and standard error of mean

In my homework, I was asked to find the standard error of mean for 2 cases and then do the 5% and 1% test for both of them. I know how to work out stand error of mean, but I don't know how to use it ...
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X and Y are two random variables, what is the standard deviation of X - 2Y

I have: E(X) = 10 E(Y) = 12 Var(X) = 4 Var(Y) = 9 covariance = 2 I know that for: ...
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Population deviation\Sample deviation

I am really stuck in checking weather something is a sample of the entire population or it is infact the polution. Suppose I make a bucket to hold a litre of water and I obtain 8 measurements to ...
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Difficulty to find the Standard Error in a simple hypothesis testing

I'm having some difficulty to solve a very simple hypothesis testing problem. $$\begin{array}{c|c|c|} & \text{X} & \text{Y} \\ \hline \text{1} & 1 & 1 \\ \hline \text{2} & 3 ...
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Relationship between median and standard deviation

I have some data and I added Gaussian noise with zero mean ($\mu=0$) and standard deviation ($SD=SD$). I was interested to see the behaviour of the noise to the data after integrations. I integrated ...
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Why does variance divide by $n-1$? [duplicate]

The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ I read that $n-1$ is used instead of just $n$ when we are measuring the variance of a sample taken from a bigger population. I don't ...
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Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are ...
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3answers
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question about Mean absolute deviation formula

$$\frac{\sum_{i=1}^{n}(x_i-\bar x)}{n}$$ This method will not work for calculating the mean deviation. Instead we have: $$\frac{\sum_{i=1}^{n}|x_i-\bar x|}{n}.$$ I'm not quite understanding why ...
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32 views

Standard Deviation ( Sort of ) Problem

I have a bunch of particles spread over a 2D area. I plan to fit a a distribution to describe the spread. To start off : I have about 100 particles arranged in a circular pattern in a "unit" ...
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Model selection: geometric mean of the standard deviation.

I have two models that represent a physical process. To determine which model is the best, I make some experiments and compare measured data with data predicted by each of the models. The model with ...
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Where are they getting this number from?

Here's the question that I'm having a problem with: ...
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Constructing confidence variances for std and variance samples.

A) Construct the 90% confidence interval for the standard deviation for the dark treatment. B) Construct the 95% confidence interval for the variance for the sunlight treatment. And that what I ...
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Statistics and data spread help?

How do you tell if the inter quartile range or standard deviation is a better spread of data?
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392 views

Probability and proportion from standard deviation and mean [duplicate]

I do not know how to start this problem-help needed-kindly help me The lifetimes of a colour TV picture tube is normally distributed, with a mean of 8 yrs and a standard deviation of 2 years. ...
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Why square the result of $x_1 - \bar{x}$ in the standard deviation? [duplicate]

I don't understand the necessity of square the result of $x_1 - \bar{x}$ in $$\sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}}$$. In fact I don't understand even why is $N - 1$ on the denominator ...
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Evaluating Data

I have a set of data that I need to evaluate. The data came from 15 people we asked to evaluate several project proposals using 6 different criteria. For each weighted criteria, they selected 1 of 4 ...
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same standard deviation but different mean

If two samples of data have the same standard deviation value but the mean of sample 1 is twice the value of sample 2 explain what the difference in sample mean values would indicate about the two ...
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Any way to simplify this expression?

So I have a vector of asset allocation weights given by $x \in R^4$ and a covariance matrix of the asset returns $\Sigma \in R^{4,4}$. I know by the spectral theorem, $\Sigma = V DV^{-1}$ and the ...
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Does it make sense to use zscore values with multiple confidence intervals?

I have a program that takes a historical dataset (e.g. muffins sold in the last week), calculates the zscore of the current value, and determines whether or not the current value is abnormal based on ...
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Using Least Squares method to determine unknown variables

Hey guys my next test is coming up and my professor gave us a study guide that we "should" be able to compete. Here is one of the questions I don't know how to attack: I dont just want an answer. I ...
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Determine the distribution underlying several given scores and their percentiles

I am trying to build a FICO score calculator that estimates one's FICO score given one's percentile from another credit report. FICO score data is kept fairly secret, but the following information is ...
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investigating a relationship at $5 \% $ level significance

$n=12$ $\bar{x}=? $ sample average = $\sigma $ standard deviation = $\alpha =$ $H_a :$ Degrees of freedom if applicable Critical value(s) = Sample mean Standard error of mean = $\frac{\sigma } ...
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Std Dev of large set

Lets assume we have a router that transmits packets at 24,000 bytes/msec and that packet lengths are uniformly distributed between 100 and 1,500 bytes. Packets are incoming to the router at a rate of ...
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2answers
66 views

Statistics: how does standard deviation measure quality - please answer everyone?

There are many types of measures of variation/dispersion from the mean, but standard deviation can be confusing. If we are measuring error/variability, then 1σ is better than 2σ. That is to say that ...
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Why the natural log is there in MLE?

Why do we use natural log for MLE?
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In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing? [duplicate]

This question has been bothering me for a while: In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing the differences (and then taking the cube ...
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How to calculate Standard Deviation without detailed historical data?

i'm taking some measurements... Let's say i don't have the luxury to store each individual value but i can only store the sum of all measures and their number (and any other such aggregate data). For ...
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