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.
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 is slightly different than for a sample from the population.
Statistics - Calculating Mean given standard deviation and percentage. - Mathematics Stack Exchange
You're given the standard deviation, and a value for the left 4% of the distribution. You can calculate (or look up) how many standard deviations away from the mean you are at 4%. More on math.stackexchange.com
[Q] What is standard deviation exactly?
SD is how much individual data points deviates (on average) from the mean of the data Not exactly, but this is a reasonably good intuition. The SD is the square root of the variance -- that is, it is the square root of the average squared distance from the mean. This will not be exactly equal to the average distance from the mean in general (by Jensen's inequality). More on reddit.com
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January 11, 2023Why does the standard deviation formula square?
This doesn't intuitively make sense, as you could just get the absolute value of the difference You could, but that wouldn't be the variance. The mean is the "center" of a sample precisely in the sense that it is the value which minimizes the sum of squared distances between the mean and the values in the sample. In order words, as soon as you accept that the mean is a good measure of location, you accept that the squared deviations are a good measure of spread. The variance (the average squared deviation) is not in the scale of the original variable (it is in squared units), and so for interpretability it is common to take the square root. If you believe that the absolute deviation is the better measure of deviation, then the median is a more sensible measure of location. More on reddit.com
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October 21, 2022[Q][D] Why are the central limit theorem and standard error formula so similar?
The CLT is about the sampling distribution of a statistic. The standard error is about the variance (or standard deviation) of a statistic. The similarity is mostly in the context of what I'd characterize as "intro stats" level, where the focus is almost entirely on means of some sort. In that context, "the" CLT (there are variants of it) says that if we're talking about a mean, then the sampling distribution will get closer and closer to a Normal distribution as the sample size increases. That Normal distribution will have a mean and a variance (or standard deviation). The standard deviation of that distribution is the standard error of the sample mean. But the sample mean will have a standard error regardless of whether the sampling distribution of the sample mean is Normal or not. And other statistics than the sample mean have a version of the CLT (with a different standard error). The difference between s and σ is the difference between talking about a sample and talking about the population. When using σ we're talking about the standard deviation of the population, of which s is an estimate. Similarly, σ/√n is the standard error of the sample mean of the population (when taking a sample of size n), but s/√n is an estimate of that value. More on reddit.com
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April 24, 2024Videos
07:14
How To Calculate The Standard Deviation - YouTube
07:49
Standard deviation (simply explained) - YouTube
Standard Deviation: Definition, Formula & Calculation Examples
How To Calculate The Standard Deviation - Clearly Explained!
How to Find Sample Standard Deviation - YouTube
05:23
How To Calculate The Standard Deviation - Clearly Explained! - YouTube
Sisu
sisu.ut.ee › measurement › 33-standard-deviation-mean
3.4. Standard deviation of the mean – Estimation of measurement uncertainty in chemical analysis
It is explained when to use the standard deviation of the individual value and when to use the standard deviation of the mean: whenever the individual result is used in further calculation the standard deviation of the individual result has to be used; whenever the mean value is used in further calculations, the standard deviation of the mean has to be used. To view third-party content, please accept cookies. Change consent ... The standard deviation s (V ) calculated using the formula 3.3 is the standard deviation of an individual pipetting result (value).
LeanScape
leanscape.io › home › lean wiki › demystifying standard deviation: a beginner’s guide
Demystifying Standard Deviation: A Beginner's Guide - LeanScape
When calculating the standard deviation for a sample of a population, we use n-1 instead of n in the denominator of the formula. This practice is referred to as Bessel’s Correction.
Published September 23, 2024
dispersion of the values of a random variable around its expected value
Wikipedia
en.wikipedia.org › wiki › Standard_deviation
Standard deviation - Wikipedia
5 days ago - which means that the standard deviation is equal to the square root of the difference between the average of the squares of the values and the square of the average value. See computational formula for the variance for proof, and for an analogous ...
Indeed
indeed.com › career guide › career development › how to calculate sample mean (with formula and examples)
How To Calculate Sample Mean (With Formula and Examples) | Indeed.com
4 days ago - Standard deviation represents the normal distribution rate for a set of data, and it is the square root of the variance. Let's look at an example:Example: The teacher uses the variance of 46 to find the standard deviation: √46 = 6.78.
National Library of Medicine
nlm.nih.gov › oet › ed › stats › 02-900.html
Standard Deviation - Finding and Using Health Statistics - NIH
In this formula, σ is the standard deviation, xi is each individual data point in the set, µ is the mean, and N is the total number of data points. In the equation, xi, represents each individual data point, so if you have 10 data points, subtract x1 (first data point) from the mean and then square the absolute value.
BYJUS
byjus.com › standard-deviation-formula
Standard Deviation Formula
September 16, 2020 - This formula is given as: \(\begin{array}{l}\sigma=\frac{1}{N}\sqrt{\sum_{i=i}^{n}f_{i}x_{i}^{2}-(\sum_{i=1}^{n}f_{i}x_{i})^{2}}\end{array} \) Also Check: Difference Between Variance and Standard Deviation · Question: During a survey, 6 students were asked how many hours per day they study on an average?
GeeksforGeeks
geeksforgeeks.org › mathematics › mathematics-mean-variance-and-standard-deviation
Mean, Variance and Standard Deviation - Definition, Formula & Examples - GeeksforGeeks
To find the standard deviation of the dataset {4, 8, 6, 5, 3, 7} with a given variance of σ² = 2.92, we use the following formula: σ = √σ2 · Given that the variance σ2 = 2.92, we can calculate the standard deviation σ: σ = 2.92 ...
Published July 23, 2025
Statistics LibreTexts
stats.libretexts.org › bookshelves › introductory statistics › introductory statistics (shafer and zhang) › 6: sampling distributions
6.1: The Mean and Standard Deviation of the Sample Mean - Statistics LibreTexts
March 27, 2023 - The standard deviation of the sample mean \(\bar{X}\) that we have just computed is the standard deviation of the population divided by the square root of the sample size: \(\sqrt{10} = \sqrt{20}/\sqrt{2}\). These relationships are not coincidences, ...
Statistics By Jim
statisticsbyjim.com › home › blog › standard deviation: interpretations and calculations
Standard Deviation: Interpretations and Calculations - Statistics By Jim
September 24, 2025 - As you can see in the formula, the standard deviation is the square root of the variance. Use my Standard Deviation Calculator to find the dispersion in your dataset! Or use the Mean Absolute Deviation Calculator.
Cuemath
cuemath.com › data › standard-deviation
Standard Deviation - Formula | How to Calculate Standard Deviation?
It is one of the basic methods of statistical analysis. Standard Deviation is commonly abbreviated as SD and denoted by the symbol 'σ’ and it tells about how much data values are deviated from the mean value. If we get a low standard deviation then it means that the values tend to be close to the mean whereas a high standard deviation tells us that the values are far from the mean value. We have separate formulas to calculate the standard deviation of grouped and ungrouped data.
Calculator.net
calculator.net › home › math › standard deviation calculator
Standard Deviation Calculator
The i=1 in the summation indicates the starting index, i.e. for the data set 1, 3, 4, 7, 8, i=1 would be 1, i=2 would be 3, and so on. Hence the summation notation simply means to perform the operation of (xi - μ)2 on each value through N, which in this case is 5 since there are 5 values in ...
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Let the weight of the chickens be $X$. Then $X \sim N(\mu,\sigma^2)$ where $\sigma = 4.2$ is the standard deviation of the weights and $\mu$ is the mean of the weights. Then, the statement you're given is $P(X < 20) = 0.04$.
Now, rewrite $P(X<20) = P(X-\mu < 20-\mu) = P( \frac{X-\mu}{\sigma} < \frac{20-\mu}{\sigma}) = P(Z < \frac{20-\mu}{\sigma})$ where $Z \sim N(0,1)$. Then, look up $c$ in a standard normal table such that $P(Z<c) = 0.04$ and then note $\frac{20-\mu}{\sigma} = c$. Solve for $\mu$, and you are done.
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You have to use the fact that the weights are normally distributed.
You're given the standard deviation, and a value for the left 4% of the distribution.
You can calculate (or look up) how many standard deviations away from the mean you are at 4%.
Given this, you multiply the number of standard deviations from the mean by the standard deviation (in lbs) to see how many lbs away from the mean you are.
You know one end (20 lbs) and you can now find the other end, which is the mean.
Outlier
articles.outlier.org › a-step-by-step-guide-on-how-to-calculate-standard-deviation
A Step-by-Step Guide on How to Calculate Standard Deviation | Outlier
June 27, 2022 - Calculating standard deviations by hand can take a lot of time and lead to many errors, especially when dealing with large data sets. Fortunately, it’s incredibly easy to calculate standard deviations using statistical software. Below are some examples of the software and commands you can use. In Excel or Google sheets, use the formula =STDEV().
BBC
bbc.co.uk › bitesize › guides › zcjv4wx › revision › 2
The formulae - Standard deviation - National 5 Applications of Maths Revision - BBC Bitesize
March 7, 2023 - Comparing these formulae with standard deviation formulae in books or in your calculator, you may notice that sometimes the \(n - 1\) in the denominator is replaced by \(n\). When you're finding the standard deviation of a set of measures, which are only a sample of the total set of measures, then it's correct to use \(n - 1\). When statisticians know they're working with the whole set or the population then they use \(n\) instead of \(n - 1\). Remember\(\sum\)means 'sum of' and \({\bar X}\) is the 'mean'.
CalculatorSoup
calculatorsoup.com › calculators › statistics › standard-deviation-calculator.php
Standard Deviation Calculator
November 4, 2025 - Standard deviation is a measure of dispersion of data values from the mean. The formula for standard deviation is the square root of the sum of squared differences from the mean divided by the size of the data set.
Investopedia
investopedia.com › terms › s › standarddeviation.asp
Standard Deviation Formula and Uses, vs. Variance
June 5, 2025 - Standard deviation is calculated by taking the square root of a value derived from comparing data points to a collective mean of a population. The formula is:
The BMJ
bmj.com › about-bmj › resources-readers › publications › statistics-square-one › 2-mean-and-standard-deviation
2. Mean and standard deviation
February 9, 2021 - As we did for continuous data, to calculate the standard deviation we square each of the observations in turn. In this case the observation is the number of visits, but because we have several children in each class, shown in column (2), each squared number (column (4)), must be multiplied by the number of children. The sum of squares is given at the foot of column (5), namely 1697. We then use the calculator formula to find the variance:and .Note that although the number of visits is not Normally distributed, the distribution is reasonably symmetrical about the mean.