dispersion of the values ​​of a random variable around its expected value

Statistical Techniques for Transportation Engineering
{\displaystyle {\sqrt {2}}\,\sigma }
{\displaystyle \sigma ={\sqrt {4}}=2.}
{\displaystyle {\sqrt {\left(e^{\sigma ^{2}}-1\right)\ e^{2\mu +\sigma ^{2}}}}\,.}
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to … Wikipedia
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Wikipedia
en.wikipedia.org β€Ί wiki β€Ί Standard_deviation
Standard deviation - Wikipedia
2 days ago - An estimate of the standard deviation for N > 100 data taken to be approximately normal follows from the heuristic that 95% of the area under the normal curve lies roughly two standard deviations to either side of the mean, so that, with 95% probability the total range of values R represents ...
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Calculator.net
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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.
People also ask

What’s the difference between standard deviation and variance?
Variance is the average squared deviations from the mean, while standard deviation is the square root of this number. Both measures reflect variability in a distribution, but their units differ: Β· Standard deviation is expressed in the same units as the original values (e.g., minutes or meters). Β· Variance is expressed in much larger units (e.g., meters squared). Β· Although the units of variance are harder to intuitively understand, variance is important in statistical tests.
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scribbr.com
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How to Calculate Standard Deviation (Guide) | Calculator & Examples
What does standard deviation tell you?
The standard deviation is the average amount of variability in your data set. It tells you, on average, how far each score lies from the mean. Β· In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.
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scribbr.com
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How to Calculate Standard Deviation (Guide) | Calculator & Examples
What is the empirical rule for data with variance 1?

Variance 1 means that the standard deviation equals 1 as well. The empirical rules says that:

  • 68% of your data lies at most one unit from the average;
  • 95% lies at most two units from the average; and
  • 99.7% lies at most three units from the average.
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omnicalculator.com
omnicalculator.com β€Ί statistics β€Ί empirical-rule
Empirical Rule Calculator
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Scribbr
scribbr.com β€Ί home β€Ί how to calculate standard deviation (guide) | calculator & examples
How to Calculate Standard Deviation (Guide) | Calculator & Examples
March 28, 2024 - Around 68% of values are within 1 standard deviation of the mean. Around 95% of values are within 2 standard deviations of the mean.
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Calculators.org
calculators.org β€Ί math β€Ί standard-deviation.php
Calculate Standard Deviation
Standard deviation (SD) measured the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (Οƒ). The following algorithmic calculation tool makes it easy to quickly discover the mean, variance & SD of a data set. Mean = sum of values / N (number of values in set) Variance = ((n1- Mean)2 + ...
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Math is Fun
mathsisfun.com β€Ί data β€Ί standard-normal-distribution.html
Normal Distribution
Let's adjust the machine so that 1000g is ... ... From the big bell curve above we see that only 0.1% are less. But maybe that is too small. ... Below 3 is 0.1% and between 3 and 2.5 standard deviations is 0.5%, together that is 0.1% + 0.5% = 0.6% (a good choice I think)
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Answers
math.answers.com β€Ί statistics β€Ί What_is_2_standard_deviations
What is 2 standard deviations? - Answers
The deviations from 100, or standard deviations, are 15. ... Trending Questions What is the definition of probability in composite risk management? Can you take the SAT more than once?
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The BMJ
bmj.com β€Ί about-bmj β€Ί resources-readers β€Ί publications β€Ί statistics-square-one β€Ί 2-mean-and-standard-deviation
2. Mean and standard deviation
February 9, 2021 - The results are given in Table ... in the logged data. The mean and median are 10.29 and 2, respectively, for the original data, with a standard deviation of 20.22....
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CalculatorSoup
calculatorsoup.com β€Ί calculators β€Ί statistics β€Ί standard-deviation-calculator.php
Standard Deviation Calculator
When working with data from a complete population the sum of the squared differences between each data point and the mean is divided by the size of the data set, n. When working with a sample, divide by the size of the data set minus 1, n - 1. ... Take the square root of the population variance to get the standard deviation. Population standard deviation = \( \sqrt {\sigma^2} \)
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Wikipedia
en.wikipedia.org β€Ί wiki β€Ί 68–95–99.7_rule
68–95–99.7 rule - Wikipedia
1 week ago - For example, Ξ¦(2) β‰ˆ 0.9772, or Pr(X ≀ ΞΌ + 2Οƒ) β‰ˆ 0.9772, corresponding to a prediction interval of (1 βˆ’ (1 βˆ’ 0.97725)Β·2) = 0.9545 = 95.45%. This is not a symmetrical interval – this is merely the probability that an observation is less than ΞΌ + 2Οƒ. To compute the probability that an observation is within two standard deviations of the mean (small differences due to rounding):
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Omni Calculator
omnicalculator.com β€Ί statistics β€Ί empirical-rule
Empirical Rule Calculator
January 18, 2024 - Intelligence quotient (IQ) scores are normally distributed with the mean of 100 and the standard deviation equal to 15. Let's have a look at the maths behind the 68 95 99 rule calculator: ... \mu + 2\sigma = 100 + 2 \cdot 15 = 130ΞΌ+2Οƒ=100...
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Davidmlane
davidmlane.com β€Ί hyperstat β€Ί A83043.html
Why 70 is 2 Standard Deviations Below the Mean
The mean is 80 and the standard deviation is 5. Since 70 is 10 points below the mean (80-70 = 10) and since a standard deviation is 5 points, there is a distance of 2 standard deviations between the 80 and 70 (10/5=2). In general, the number of standard deviations a score is from the mean can be computed using the formula where z is the number of standard deviations above the mean (ΞΌ) the score X is.
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Investopedia
investopedia.com β€Ί terms β€Ί e β€Ί empirical-rule.asp
Empirical Rule: Definition, Formula, and Example
May 21, 2025 - It indicates that 68% of observations will fall within the first standard deviation (Β΅ Β± Οƒ) in normal distributions, 95% within the first two standard deviations (Β΅ Β± 2Οƒ), and 99.7% within the first three standard deviations (Β΅ Β± 3Οƒ) ...
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Stack Exchange
math.stackexchange.com β€Ί questions β€Ί 3418406 β€Ί what-does-the-two-standard-deviations-from-the-mean-means-according-to-statistic
What does the two standard deviations from the mean means according to statistics and probability? - Mathematics Stack Exchange
Grades distributions are often either approximately normal or adjusted to be normal (so I'm told), and thus if a student scored two standard deviations above the mean, then this means they scored in the top $\frac{1-0.95}{2}=$2.5% of students.
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Math is Fun
mathsisfun.com β€Ί data β€Ί standard-deviation-formulas.html
Standard Deviation Formulas
We already calculated (x1-7)2=4 etc. in the previous step, so just sum them up: = 4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9 = 178 Β· But that isn't the mean yet, we need to divide by how many, which is done by multiplying by 1/N (the same as dividing by N): ... But wait, there is more ... ... sometimes our data is only a sample of the whole population. ... We can still estimate the Standard Deviation.
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YouTube
youtube.com β€Ί watch
12.4.2 Standard Deviations Above and Below the Mean - YouTube
Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.
Published Β  June 17, 2020
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Utah
soc.utah.edu β€Ί sociology3112 β€Ί normal-distribution.php
The Normal Distribution - Sociology 3112 - Department of Sociology - The University of utah
One step to the right or one step to the left is considered one standard deviation away from the mean. Two steps to the left or two steps to the right are considered two standard deviations away from the mean. Likewise, three steps to the left or three steps to the right are considered three ...