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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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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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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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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61 views

Where are they getting this number from?

Here's the question that I'm having a problem with: ...
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727 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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4answers
310 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 \left(X_i-\bar{X}\...
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5answers
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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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17 views

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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246 views

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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1answer
303 views

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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1answer
36 views

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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1answer
60 views

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
1k 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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5answers
219 views

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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1answer
2k views

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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645 views
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Standard Deviation result wrong or right

I made two scripts in PHP to calculate the standard deviation. But I am not sure if it works correctly both of my scripts have different results. first script 1,2,3,4,5,1 = 1.5 second script 1,2,3,4,...
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0answers
76 views

Have averages, need variance

I have a large spreadsheet, generated by a colleague, that contains the results of $E$ experiments. For each experiment, he calculated the average of $M$ measurements. I need the calculate the ...
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1answer
38 views

Standard deviation / Bell Shaped Distribution

In a forest, it is known that the circumference of 10 year old oak trees when measured three feet above the ground is 20 inches with a standard deviation of 4.5 inches. It is also known that these ...
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1answer
491 views

Why is the expected value of the squared value equal to the sum of the standard deviation and the mean?

I am currently reading the proof here that one has to divide by $n-1$ in order to get an unbiased estimator of the population variance. What I do not get is this: \begin{equation}E[y_i^2] = \sigma^2 ...
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standard deviation of a rate of phone calls

I am trying to implement some real time monitoring. I have a real time data feed from which I can calculate the number of phone calls received in the last hour (now-60 minutes). I want to alert when ...
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Why is my sample standard deviation not an unbiased estimator?

I was goofing around with a spreadsheet and decided to show empirically that the sample standard deviation is an unbiased estimator of the true population standard deviation. Link to Excel File I ...
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65 views

Standard deviation and intervals

I'm working on some homework and I'm stuck on a question that is not making sense to me in terms of my answer. The question states: ...
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66 views

Chebychev to get at least 90 %

Im am given a list of integers and asked to give the interval that contains at least 90 % of my values. Values : $62,56,72,83,66,77,62,71,50,58, 74,81,76,67,70,70,69,67,80,81, 74,53,73,55,66,88,73,...
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Standard Deviation Question

My working out: Median = mean = 60 Q3 = 25% of values at 75 25% = 0.25 = z-score of 0.68 Sx = (75-60)/0.68 = 22.3881 approx = 20... I said D The correct answer is B. 10
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190 views

Weighted mean from a set of average and standard deviation pairs

I'm trying to replicate some math a professor did related to Twitter sentiment analysis. Basically, there is a sentiment dictionary, called ANEW, that contains a mean and standard deviation for 3 ...
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266 views

Standard Deviation for Normally Distributed Bell Curve - Worded Problem

My working out: Z = (14-9.5)/2.25 = 2 % less than 2 = 95% Answer is 97.5 % .... no idea...
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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 ...
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52 views

Summing up Standard Deviations - best approximation

For a long data series the overall Standard Deviation shall be collected. However, due to memory constraints the data has to be aggregated per day - in a way that only one number is stored per day (...
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153 views

Given Standard Deviation and Population size, how can I calculate the number of population at mean

As per the title, I'd like to calculate the number of the population at mean, given a std.dev and population size. The use case for this, is Mobile Phone push notifications. I send the notification ...
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36 views

How to answer probability question with basic std dev statistics

I have a data sample, say: $69$, $72$, $100$, $87$, $57$, $123$, $110$. Knowing the standard deviation and the mean what is the answer to the question: What is the number ($x$) for which $n\%$ out ...
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1answer
370 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 ...
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1answer
41 views

Standard deviation: When to use which sum-coefficient?

I'm wondering when to use $\sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ and when to use $\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(X_{i}-X_{mean})^2}$ which I have both seen in ...
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1answer
190 views

How is the Standard Error and the Unbiased Estimate of the Variance Related?

I am going through a statistics textbook and there are two similar formula's that I cannot seem to grasp, one under the "Sampling Error" section and the other under the "Unbiased Estimator" section. ...
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2answers
52 views

Find the variance of $x$ when the standard deviation is given in the form of $ax+b$.

The standard deviation of $3x+7$ is $4$; then what is the variance of $x$? I know that variance is the square of the standard deviation but how does $3x+7$ and $x$ relate?
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Rolling standard deviations

I am trying to calculate standard deviations on an array of numbers. My psuedo code looks like this: ...
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139 views

can STD of subsets be used to arrive at the STD of the whole set

Assuming I have a set of values called S and the STD of S is Xs. Let's say I split S into two subsets S1 and S2 with standard deviations X1 and X2. The number of elements in S1 and S2 are called W1 ...
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117 views

The rule of the 3 sigmas -— how many times multiply the sigma to get 85%?

$\sigma c=\sqrt{\overline{R}(\sigma S)^{2}+\overline{S^{2}}(\sigma R^{2})}$ where, $\sigma c$ --- the buffer stock --- needed for maintaining the risk of stockouts, is used by logistitians $\...
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41 views

Confidence interval and normal distribution

For question (a), is the answer 0.7143? For question (b), is the answer 10.85 and 11.95 ?
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48 views

I need a probability statement

I need some help with this question please. Make a probability statement about a group of workers who produced product data with a mean of 20 and a standard deviation of 1.03.
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60 views

Standard Deviation: Can I remove some data?

Suppose That I have measured property "X" in 16 points of a rigid body. This rigid body is consisted of two different materials. In one of them, property X is around 1, and in the other X is around 5. ...
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2answers
983 views

Normalizing data to a given value.

I would like compare the data by normalizing it to a given value. for example: [20,30,40,50,60,70] How do I normalize the given set of elements to its first value, ...
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1answer
35 views

mean and standard deviation of students taking a test

6 percent of all students of a class will not pass a test. There are 450 students taking this test. Let X represent the number, out of 450 students, who will pass this test. Find the mean and standard ...
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1answer
41 views

Solving Probability using standard Deviation and Mean

Given a normal random variable with mean 90 and a standard deviation 3, find the probability that x is greater than or equal to 86.67 and less than or equal to 96.33
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Exclude an RGB color from a set

I'm currently implementing an algorithm to split an image into smaller chunks, based on straight line separators. Here's the image I'm processing. It's very small, so you may want to save it and ...
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1answer
59 views

Calculation the Standard Deviation

I want to calculate the standard deviation of the following numbers: 30, 45, 45, 60, 75, 80, 90, 100, 110, 120. As far as I know, that would be $\sqrt{\frac{1}{10}(...