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Standard Deviation Calculator
This free standard deviation calculator computes the standard deviation, variance, mean, sum, and error margin of a given data set.
dispersion of the values of a random variable around its expected value
Wikipedia
en.wikipedia.org › wiki › Standard_deviation
Standard deviation - Wikipedia
6 days ago - For unbiased estimation of standard deviation, there is no formula that works across all distributions, unlike for mean and variance. Instead, s is used as a basis, and is scaled by a correction factor to produce an unbiased estimate.
what actually is standard deviation? I know the steps of calculating it and applying it. I have heard it can be USED to tell how well your sample fits, but what the hell IS it?
It's vaguely, intuitively --- not accurately --- the average distance from the mean the data are. I think for these statistics, it's best to accept that it is just what it is. It is it's formula to calculate it. After you use it a bit, and see where else it pops up in statistics, it makes more sense why it's calculated the way it is. More on reddit.com
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October 30, 2025Understanding standard deviation formula
It is possible to use Mean Absolute Deviation instead! And maybe in some alternate universe, that would be the value chosen to be the "standard deviation". But squaring instead of absolute-value-ing gives us a bunch of nice properties. Absolute value is hard to work with due to its "pointiness". Squaring is easy to work with. For instance, we can think about least squares regression - this is where we have a bunch of data points, and we want to fit a line to them. The line predicts a certain y-value for every x-value, but it might not be exactly the same. We can look at the 'error' in each of our predictions - this gives us a data set. We want this data set to have a mean of 0, and a small deviation from 0, to get the best possible fit. It turns out that it's very easy to do this if we choose standard deviation as our measurement of deviation: there's a nice formula involving a few matrix multiplications. It's easy to do on a computer. But if we chose MAD, there's no nice and easy formula. A bunch of other similar things go the same way: with squares, they're [relatively] easy, and with absolute value, they may not even have a 'nice' solution. More on reddit.com
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June 6, 2025How to calculate average Standard Deviation ?
You're looking for the pooled variance: https://en.wikipedia.org/wiki/Pooled_variance Pooled variance is a weighted average of each variance, weighted by the degrees of freedom (n-1) of each set. Once you have the pooled variance, you can take the square root to get the pooled standard deviation. Say you have two data sets: n_1 = 10; mean_1 = 15; sd_1 = 3 n_2 = 15; mean_2 = 12; sd_2 = 2 Then the pooled variance would be: sd_p2 = ( (10-1)*32 + (15-1)*22 ) / (10+15-2) sd_p2 = 5.956521739 And then take the square root to get the pooled standard deviation: sd_p = 2.440598644 Notice that the pooled standard deviation is closer to the second set, because the second set is bigger. Also notice that the mean doesn't factor into the calculation. More on reddit.com
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January 22, 2016ELI5: Standard Deviation
Standard Deviation is a measure of how much variation exists in a set of data. A low SD means that most of the data lies close to the mean (Mathematical Average). Example data (5,5,5,6,7,7,7) A High SD means that the data is more spread out. Example data (1,1,1,6, 11,11,11) Both have a mean (Mathematical Average) of 6, but the SD of the first is .93 and the second is 4.6. More on reddit.com
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March 28, 2014Videos
JMP
jmp.com › en › statistics-knowledge-portal › measures-of-central-tendency-and-variability › standard-deviation
Standard Deviation
The Σ symbol is the summation symbol; in this formula, it means that each of the squared differences between a data value and the sample mean should be added up, just as in the example. In the rare situations where you have data for the entire population, the calculation of the standard deviation ...
National Library of Medicine
nlm.nih.gov › oet › ed › stats › 02-900.html
Standard Deviation - Finding and Using Health Statistics - NIH
The first step is to subtract the mean from each data point. Then square the value before adding them all together. Now divide by 9 (the total number of data points) and finally take the square root to reach the standard deviation of the data:
Laerd Statistics
statistics.laerd.com › statistical-guides › measures-of-spread-standard-deviation.php
Standard Deviation | How and when to use the Sample and Population Standard Deviation - A measure of spread | Laerd Statistics
Therefore, you would normally calculate the population standard deviation if: (1) you have the entire population or (2) you have a sample of a larger population, but you are only interested in this sample and do not wish to generalize your findings to the population.
University of Southampton Library
library.soton.ac.uk › variance-standard-deviation-and-standard-error
Maths and Stats - Variance, Standard Deviation and Standard Error - LibGuides@Southampton at University of Southampton Library
November 10, 2025 - Standard deviation is the square root of the variance, and therefore is also a measure of spread - more specifically, it is a measure of dispersion (or, the measure of variability!). Where variance is used to show how much the values in a dataset vary from each other, the standard deviation exists to show how far apart the values in a dataset are from the mean, and therefore can be used to identify outliers.
Standard Deviation Calculator
standarddeviationcalculator.io
Standard Deviation Calculator - Sample/Population
Step 2: Calculate (xi - µ) by subtracting the mean value from each value of the data set and calculate the square of differences to make them positive. Step 3: Get the sum of all values for (xi - µ)2. ... Step 4: Divide ∑(xi - µ)2 with (N). ... Step 5: Take the square root of ∑(xi - µ)2/N ...
Cuemath
cuemath.com › data › standard-deviation
Standard Deviation - Formula | How to Calculate Standard Deviation?
As discussed, the variance of the data set is the average square distance between the mean value and each data value. And standard deviation defines the spread of data values around the mean. Here are two standard deviation formulas that are used to find the standard deviation of sample data and the standard deviation of the given population.
YouTube
youtube.com › datatab
Standard deviation (simply explained) - YouTube
The most common measures of dispersion for metric variables are the standard deviation and the variance in statistics. These two measures relate each express...
Published September 19, 2021 Views 918K
Texas A&M University
chem.tamu.edu › class › fyp › keeney › stddev.pdf pdf
Average, Standard Deviation and Relative Standard Deviation
data, then calculating the average, standard deviation, and relative standard deviation.
Hunter College
hunter.cuny.edu › dolciani › pdf_files › brushup-materials › calculating-variance-and-standard-deviation.pdf pdf
Calculating Variance and Standard Deviation
Skip to content. | Skip to navigation · About Mary P. Dolciani DMLC Mission
CalculatorSoup
calculatorsoup.com › calculators › statistics › standard-deviation-calculator.php
Standard Deviation Calculator
November 4, 2025 - Standard deviation of a data set is the square root of the calculated variance of a set of data. The formula for variance (s2) is the sum of the squared differences between each data point and the mean, divided by the number of data points.
Reddit
reddit.com › r/askstatistics › what actually is standard deviation? i know the steps of calculating it and applying it. i have heard it can be used to tell how well your sample fits, but what the hell is it?
r/AskStatistics on Reddit: what actually is standard deviation? I know the steps of calculating it and applying it. I have heard it can be USED to tell how well your sample fits, but what the hell IS it?
October 30, 2025 - There is a caveat. In step 3, instead of dividing by n, we would usually divide by n - 1 as you pointed out. That's because there are two standard deviation formulas: one for dividing by n (called population standard deviation) and one for dividing by n - 1 (called sample standard deviation).
YouTube
youtube.com › shorts › KJwUK3tnnSE
How to Find Sample Standard Deviation - YouTube
December 14, 2023 - Finding sample standard deviation is pretty easy, but doing it by hand can take a long time. This is a simple example of sample standard deviation. We simply...
Math is Fun
mathsisfun.com › data › standard-deviation-formulas.html
Standard Deviation Formulas
To calculate the standard deviation of those numbers: 1. Work out the Mean (the simple average of the numbers) 2. Then for each number: subtract the Mean and square the result · 3. Then work out the mean of those squared differences. ... The formula actually says all of that, and I will show you how.
DataCamp
datacamp.com › tutorial › standard-deviation-excel
How to Calculate Standard Deviation in Excel | DataCamp
August 5, 2024 - In contrast, STDEV.S() calculates the standard deviation for a population sample and divides it by the number of data points minus one (N-1) to account for sample variability, also known as Bessel's correction. ... Arunn ThevapalanSenior Data Scientist & Technical Writer. Helping data enthusiasts break into data science. ... 0 minGain the essential skills you need to use Excel, from preparing data to writing formulas and creating visualizations.
Reddit
reddit.com › r/learnmath › understanding standard deviation formula
r/learnmath on Reddit: Understanding standard deviation formula
June 6, 2025 -
For context I’m at a calculus 1 level math, nothing too advanced. I understand conceptually that standard deviation is the average distance a point will be from the mean of a data set. I know that in the formula, x-μ is squared because it makes it positive, at least as far as I understand.
Why isn’t it possible to use the absolute value of x - μ divided by n? Wouldn’t that simply find the average distance from the mean? Is there another reason to square x - μ besides making it positive? I’ve heard of the absolute deviation formula, but I’m confused why that isn’t standard, if you’re just trying to find the average dispersion from the mean.
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It is possible to use Mean Absolute Deviation instead! And maybe in some alternate universe, that would be the value chosen to be the "standard deviation". But squaring instead of absolute-value-ing gives us a bunch of nice properties. Absolute value is hard to work with due to its "pointiness". Squaring is easy to work with. For instance, we can think about least squares regression - this is where we have a bunch of data points, and we want to fit a line to them. The line predicts a certain y-value for every x-value, but it might not be exactly the same. We can look at the 'error' in each of our predictions - this gives us a data set. We want this data set to have a mean of 0, and a small deviation from 0, to get the best possible fit. It turns out that it's very easy to do this if we choose standard deviation as our measurement of deviation: there's a nice formula involving a few matrix multiplications. It's easy to do on a computer. But if we chose MAD, there's no nice and easy formula. A bunch of other similar things go the same way: with squares, they're [relatively] easy, and with absolute value, they may not even have a 'nice' solution.
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The historical answer is that squares are just easier to work with mathematically than absolute values. They play nice with derivatives and are therefore easier to minimize. So mathematicians ended up using them as the standard. The deeper motivation for using a sum of squares will probably be hard to understand without some linear algebra knowledge, but the general idea is that the standard deviation is a kind of distance (or vector length), and using Pythagoras to calculate it is the more natural choice. So you end up with an expression like √(a2 + b2 + c2 + d2 + ...) in the formula where [a, b, c, d, ...] are the components of the vector. This is the Pythagorean theorem in arbitrary dimensions. In this case, we're calculating a distance from the mean so the components look like [a - μ, b - μ, c - μ, d - μ, ...]. It's of course entirely possible to use a different metric to measure distances, such as the Manhattan metric which simply adds up the distance along each component like |a| + |b| + |c| + |d| + ..., but this is not the natural choice.
Math is Fun
mathsisfun.com › data › standard-deviation.html
Standard Deviation and Variance
The Standard Deviation is a measure of how spread out numbers are. ... The formula is easy: it is the square root of the Variance.