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 the standard deviation is not as the same as online calculator

I need to calculate the standard deviation for these numbrs: -12 -3 0 -13 8 -6 0 -22 -1 7 -7 1 -2 -13 -4 0 -6 -4 -10 3 I did everything, but still my answer is ...
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What to call & how to compute errors in a very asymmetric sample

Consider the following sample $\{1.25,1.5,1.75,2.0,2.25,2.5,2.75,10.\}$. Mean is $\mu=3.$, standard deviation is $\sigma\approx 2.69$. I am wondering how to compute and what to call error bars in the ...
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What is meant by statisticians when they talk about between population differences vs within population differences?

Suppose we have two populations of people in different parts of the world and we want to talk about the variation in heights between the two populations. As I understand it, statisticians are talking ...
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Statistics- Finding Probability

A local lawn service has determined the average time it takes to mow an average residential yard is thirty-five minutes. If mowing times are independent and constant, what is the probability it will ...
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A casino owner is concerned based on past experience that his dice show 6 too often

Currently I am trying to understand hypothesis testing, but I have a problem with the following question: A casino owner is concerned based on past experience that his dice show 6 too often. He makes ...
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Statistics of several small datasets

I have 3 different datasets, each with 5 datapoints with a certain error. In theory, all the datapoints should have the same value, even from the different datasets (So, ideally I end up with 15 the ...
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Will calculating standard deviations from percentages give different results to claculating them from the raw data?

I'll start off by saying I am not a mathematician, nor have I studied maths for many years, so please keep the answers simple :) I am working with data that has a geographical context. So assume I ...
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Probability involving Normal Distribution

Two instruments are used to measure the height, h, of a tower. The error made by the less accurate instrument is normally distributed with mean 0 and standard deviation 0.0056h. The error made by the ...
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How do I calculate if a line on a graph is generally far away from another line?

disclaimer: I'm (evidently) not a mathematician/statistician and a total n00b so if this question is too basic for the community let me know! Also excuse any misuse of terminology! Say I have two ...
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Sum of Two Normal Distributions - Weighted?

The problem is given as such: John owns a portfolio with two stocks, ABC and XYZ. He has invested \$400 in ABC and \$600 in XYZ. The quarterly return on ABC is normally distributed with a mean of 7% ...
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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 ...
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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 ...
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Geometric Mean of Random Variables

I measure a series of $n$ objects [O_1, O_2, O_3, ..., O_n]. Because those measurements are quite hard to perform, I have quite a lot of measurement error and ...
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Standard distribution formulae trick

I am trying to understand the following question. The height of adult males is normally distributed with a mean of 172cm and standard deviation of 8cm. If 99% of adult males exceed a certain height, ...
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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 ...
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Estimate of group standard deviation given pairs of distances

I'm trying to find how much the errors associated with a specific method of estimating a collection of values will decrease, when I add additional data to make a "better" estimate. In particular, ...
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what's the best way to find a central tendency and filter outliners for this given problem?

I'm faced with the following problem: I have a group of Nodes which belong in the same network. They are constantly talking with one another providing services to one another. Suppose nodeA asks for ...
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Finding the Correct Sample Size N to calculate the $SEM$ in a Relative A/B Test with $X \sim B(p_1,n_1)$ and $Y \sim B(p_2,n_2)$

I asked a similar question on Cross Validated but since I'm more interested on the theory behind choosing the right $N$, I decided to also post it here. For the test, I randomly assign users to two ...
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Deal with circular standard deviation

I have a sensor that gives me a direction of the target in degrees with a certain standard deviation and I use a circular probability density function (PDF) to represent probable locations for the ...
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Standard deviation of a normal distribution with arbitrary points

Good day! Im currently dealing with the formula in determining the expected number of real roots of random algebraic polynomial,,, and I want to solve for the formula of the standard deviation. I have ...
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A Gaussian Divided by a Gaussian Equal to A Gaussian Divided by a Constant

I have a neural-network model in which each neuron is associated with an angle $\theta$. Firing rate as a function of $\theta$ is either a Gaussian or a constant. The claim has been made using this ...
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Why do RMS and Standard Deviations sum squares?

I've seen some references to this - or a few examples of it, but for some reason it's not clicking. Can anyone give me a good layman's explanation of why calculations such as RMS values and Standard ...
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What is Bootstrapping in statistics? How can I use it to determine error in the mean, variance, kurtosis and skewness of a data set?

From what I understood from searching randomly is that it has something to do with resampling. What does this resampling mean? Is it selecting random data from a distribution or is it getting data ...
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finding min and max after removing percentage of num values knowing the standard deviation.

I have a question i have some data and i know it's (number of values, min, max, mean and standard deviation) can I know the minimum after removing x% of the total number of values and the maximum ...
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Standard deviation: calculating how polarizing a question is

I'm trying to calculate how polarizing a question is. Let's say I have a question that has 3 possible choices. A certain percentage of people choose a specific answer. Answer a: $30\%$ Answer b: ...
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Standard Error for Weighted Values

I want to calculate the standard error for an experimental measurement. The data is stored as a 2D image which is circularly symmetric about a center point. To reduce the data we radially integrate ...
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Comparing Curves

I am trying to compare a company's revenue to some economic indicators such as DJ index and S&P 500 index. I came up with a way to plot the three lines on the same scale. Here's the table. What ...
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How to compare dispersion of data?

From my statistic book, I learn that standard deviation is used to estimate how much the data spread around the mean value. If I have two or more sets of data, for each one, they normalized to the ...
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Estimating population standard deviation with sample standard deviation

At 4:30 of this video the author decided to estimate the standard deviation of the population with sample standard deviation (sample size was $100$). In the next video, the author mentioned that it ...
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Finding an interval estimate for $\mu$ given a sample size and variance

I'm in a statistics class and am doing a problem for homework about confidence intervals. I don't really know what it's asking though or when I've even reached a valid solution. The problem says: ...
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Formula to get mean and standard deviation of this multi-variable equation

$$ \binom n x \times\left(\frac1r\right)^x\times\left(\frac{r-1}r\right)^{n-x} $$ If you have $n$ boxes and have a $\frac1r$ chance to fill each one, this equation returns the chance that you fill ...
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CV Percentage Error with Confidence Variable

I am trying to calculate a confidence variable (CV %) of two numbers where the numbers them selves have a confidence range. Appologies for my sloppy representation, I am somewhat of an equation novice ...
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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 ...
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Are there any limits on Standard Deviation of a data set with given $n$ and mean?

Say a class of 200 students is graded out of 100 marks. The mean of the dataset is 50. Can we put a maximum limit on Standard Deviation for the set ? I thought of putting a number of people onto 100 ...
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Use of normal distrubution to determine price differences

Currently I am analyzing price data of many of our competitors. For example: Company A sells product X for $45 Company B sells product X for $44 Company C sells product X for $52 We sell product ...
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Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ...
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Discrepancy between different methods for finding standard deviation?

I can't see where I am going wrong. There are two different ways of writing the standard deviation: $ \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i – \overline{x})^2}$ $ \sigma = ...
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Trouble understanding when to use ANOVA to analyse variances?

I'm having trouble knowing when to use the ANOVA method for analysing variances. For example this question: $1.$ In an investigation of the effect of large amounts of lime on marigolds, the numbers ...
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Standard deviation of the mean of sample data

I can't quite understand what this formula means: $$\sigma_{\overline{x}}=\frac{\sigma}{\sqrt n}$$ I know what standard deviation $\sigma$ is - it's the average distance of my data points (samples) ...
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Standard Deviation: Population versus Sample (specific example)

So, I'm trying to use a t-test to test a hypothesis regarding information: My students were given a question in which they chose either $1, 2, 3, 4$, or $5$ to determine how much they enjoyed my ...
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Calculating uncertainty in standard deviation

I have a distribution with literally an infinite number of potential data points. I need the standard deviation. I generate about a hundred points and take the standard deviation of the points. ...
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Lower std.deviation of a distribution?

How would one lower the std.dev => $\sigma$ for an arbitrary distribution? The reason why I ask, is because I have a distribution which tend to get far above my threshold value, and i am running out ...
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Calculate mean and std.dev from a lot of coordinates

How do i calculate the mean coordinate and the standard deviation of a cloud of (x,y) coordinates. I know how to calculate the mean, but i am struggling with calculating the std. deviation.
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Probability mean,variance and standard deviation formula confusion.

I have a confusion in the formula attached. Why and how are the two formulas equivalent ? sigma in the image is the standard deviation of a distribution...
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Width of Gaussian distribution from N trials of coin tossing

What is the width of the Gaussian distribution that is generated from performing $N$ trials of coin tossing? Example: In a trial of 1000 tosses of a coin, $P(H)=0.5$ and $P'(H)=0.5$, where $H$ refers ...
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Chebyshev's inequality for 1 standard deviation results in 0?

In applying Chebyshev's inequality to a probability distribution, the following is the given equation: $$p(\mu - c*\sigma \le X \le \mu + c*\sigma) \ge 1 - \frac{1}{c^2}$$ This indicates for any ...
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Method for determining the average deviation of data values over time?

I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet. For convenience, I've set the minimum and maximum values on the y-axis to the weights that ...
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Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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What are the bounds on Variance?

I have an image which can be considered as a 2D plane. Now, I have to check the variance of some points which are distributed over this 2D plane. TASK: I want to calculate the variance to predict if ...
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Finding the probability of loss from standard deviation in normal distribution

I am unsure how to approach the following question. The returns from a project are normally distributed with a mean of \$220,000 and a standard deviation of \$160,000. If the project loses more than ...