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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.

Standard deviation

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
3 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 ...
Relationship with standard error and statistical significance
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Definition of population values
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Interpretation and application
Standard deviation matrix
Relationship between standard deviation and mean
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Standard deviation index
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Videos
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The mean and standard deviation of a group of 100 observations ...
June 4, 2017
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The mean and standard deviation of 20 observations are found to ...
June 4, 2017
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The mean and standard deviation of 100 observations were calculated ...
June 22, 2018
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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
scribbr.com β€Ί home β€Ί how to calculate standard deviation (guide) | calculator & examples
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
scribbr.com β€Ί home β€Ί how to calculate standard deviation (guide) | calculator & examples
How to Calculate Standard Deviation (Guide) | Calculator & Examples
What is the empirical rule?
The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution: Β· Around 68% of values are within 1 standard deviation of the mean. Β· Around 95% of values are within 2 standard deviations of the mean. Β· Around 99.7% of values are within 3 standard deviations of the mean. Β· The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that don’t follow this pattern.
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scribbr.com
scribbr.com β€Ί home β€Ί how to calculate standard deviation (guide) | calculator & examples
How to Calculate Standard Deviation (Guide) | Calculator & Examples
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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....
Find elsewhere
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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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Brainly
brainly.com β€Ί mathematics β€Ί college β€Ί with a mean of 100, find the score that is 2 standard deviations below the mean if the standard deviation is 26.
[FREE] With a mean of 100, find the score that is 2 standard deviations below the mean if the standard deviation - brainly.com
Given: Mean (ΞΌ) = 100 Standard ... to find the score that is 2 standard deviations below the mean, we subtract 2 times the standard deviation from the mean....
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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):
Proof
Cumulative distribution function
Normality tests
Table of numerical values
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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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GeeksforGeeks
geeksforgeeks.org β€Ί data science β€Ί z-score-in-statistics
Z-Score in Statistics | Definition, Formula, Calculation and Uses - GeeksforGeeks
July 12, 2025 - For example, a Z-score of 1.5 means the data point is 1.5 standard deviations above the mean. Negative Z-Score: A negative Z-score indicates that the data point is below the mean. For example, a Z-score of -2 means the data point is 2 standard ...
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Stack Exchange
stats.stackexchange.com β€Ί questions β€Ί 17349 β€Ί how-to-interpret-two-standard-deviations-below-the-mean-of-a-count-variable-bei
How to interpret two standard deviations below the mean of a count variable being less than zero? - Cross Validated
Top answer
1 of 1
10

The short answer, is no, it is not an error.

As @whuber notes, there is nothing surprising (at least to a statistician) about the fact that two standard deviations below the mean of a count variable could be a negative value. Thus, to answer your question, perhaps it would be more useful to ponder why you might find the result surprising.

Why you might be surprised

  • Many introductory statistics textbooks show how you can use the mean, standard deviation, and the normal distribution to make claims like approximately 2.5% of the sample is expected to score below two standard deviations below the mean. You may have generalised this idea to a variable where the assumptions of such a procedure are invalid.
  • If you did this, you would be saying to yourself: "this is strange, how is it possible for 2.5% of the data to have counts below -0.6".

Estimating percentiles for counts

  • Your variable is not normally distributed, it is a count variable. It is discrete; it is a non-negative integer. Thus, in order to estimate the percentage that is greater than or equal to a given value, you need an approach suited to counts. A basic approach would involve using the sample data to estimate such percentiles. More sophisticated approaches could involve developing a model of the distribution suited to counts, justified by the data and knowledge of the phenomena, and estimated using the sample data.
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Penn State University
online.stat.psu.edu β€Ί stat200 β€Ί lesson β€Ί 2 β€Ί 2.2 β€Ί 2.2.7
2.2.7 - The Empirical Rule | STAT 200
On a normal distribution about 68% of data will be within one standard deviation of the mean, about 95% will be within two standard deviations of the mean, and about 99.7% will be within three standard deviations of the mean
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Annenberg Learner
learner.org β€Ί wp-content β€Ί uploads β€Ί 2019 β€Ί 03 β€Ί AgainstAllOdds_StudentGuide_Unit08-Normal-Calculations.pdf pdf
Unit 8: Normal Calculations | Student Guide | Page 1
Now, measure out two standard deviations from the mean, from 55.4 inches to 72.2 inches.
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University of Delaware
www1.udel.edu β€Ί htr β€Ί Statistics β€Ί Notes β€Ί class12.html
Public Management Statistics Class 12 Notes
One can think of the area under ... the curve: The area within plus and minus two standard deviations of the mean constitutes about 95 percent of the area under the curve (see Figure 2)......
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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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Khan Academy
khanacademy.org β€Ί math β€Ί statistics-probability β€Ί summarizing-quantitative-data β€Ί variance-standard-deviation-population β€Ί a β€Ί calculating-standard-deviation-step-by-step
Standard deviation: calculating step by step (article)
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Soft Schools
softschools.com β€Ί math β€Ί probability_and_statistics β€Ί the_normal_distribution_empirical_rule
The Normal Distribution - Empirical Rule
The scores that are two standard deviations of the mean range from 70 to 130 since 100 - 2(15) = 70 and 100 + 2(15) = 130. From the Empirical Rule, we know that about 95% of all students' IQ scores will fall within this range. Thus, about 950 of the 1,000 students IQ scores fall in this range.
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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.