dispersion of the values of a random variable around its expected value
Wikipedia
en.wikipedia.org › wiki › Standard_deviation
Standard deviation - Wikipedia
2 days ago - 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 be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that ...
Investopedia
investopedia.com › terms › s › standarddeviation.asp
Standard Deviation Formula and Uses, vs. Variance
June 5, 2025 - Standard deviation is a statistic measuring the dispersion of a dataset relative to its mean. It is calculated as the square root of the variance. Learn how it's used.
[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, 2023ELI5: What is standard deviation?
Two groups of students take an exam.
Group A averages 70%. Nearly every student gets a score of like 67%, 71%, 73%, etc.
Group B averages 70%. A lot of students get 100s, but a lot of other students bomb the test and get 40%.
If you look only at the average, the two groups look the same - they both averaged a 70. But they're not the same. Group B has a bunch of geniuses and a bunch of idiots, while Group A has mostly average people.
The standard deviation is a measure of how "spread out" the data is. A low standard deviation means that most of the data points are very close to the average, while a high standard deviation means that there's a lot of data that's spread out far from the average. So Group B has a much higher standard deviation than Group A.
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October 11, 2016What 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. · 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.
scribbr.com
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How to Calculate Standard Deviation (Guide) | Calculator & Examples
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: · Standard deviation is expressed in the same units as the original values (e.g., minutes or meters). · Variance is expressed in much larger units (e.g., meters squared). · Although the units of variance are harder to intuitively understand, variance is important in statistical tests.
scribbr.com
scribbr.com › home › how to calculate standard deviation (guide) | calculator & examples
How to Calculate Standard Deviation (Guide) | Calculator & Examples
What is a normal distribution?
In a normal distribution, data are symmetrically distributed with no skew. Most values cluster around a central region, with values tapering off as they go further away from the center. · The measures of central tendency (mean, mode, and median) are exactly the same in a normal distribution.
scribbr.com
scribbr.com › home › how to calculate standard deviation (guide) | calculator & examples
How to Calculate Standard Deviation (Guide) | Calculator & Examples
Videos
University of Waterloo
uwaterloo.ca › teaching-assessment-processes › about-standard-deviation
About the standard deviation | Teaching Assessment Processes | University of Waterloo
October 6, 2023 - Standard deviation indicates the variability of data—the degree to which SCP scores vary around the mean. A higher standard deviation means that there is high variability in the data. A lower standard deviation means that there is less variability in the data.
Reddit
reddit.com › r/statistics › [q] what is standard deviation exactly?
r/statistics on Reddit: [Q] What is standard deviation exactly?
January 11, 2023 -
So the way I've had it explained to me is that SD is how much individual data points deviates (on average) from the mean of the data set.
If we take 9 data points
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The mean here is 0.
When I use the excel function for SD it gives me 2,73...
By the definition I gave earlier. Shouldn't the standard deviation be somewhere between 2 and 2.5? Why 2,73?
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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).
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Standard deviation is just one of several methods to represent variation. It does not exactly match up to anything intuitive except that around 66% and 95% of data is within 1 and 2 standard deviations of the mean (when the data is normally distributed). It is used so much because it is also the square root of the variance, a value that has useful mathematical properties which are is the basis of many statistical tests. If you want to see a bit more about estimates of variation, I put a couple of videos about what summary statistics represent on YouTube. There's a discussion of standard deviation and variance in them. Conceptual introduction: https://youtu.be/GeMb6qpRMn0 Step-by-step examples: https://youtu.be/KZM42SyNmfw
National Library of Medicine
nlm.nih.gov › oet › ed › stats › 02-900.html
Standard Deviation - Finding and Using Health Statistics - NIH
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.
Cambridge Dictionary
dictionary.cambridge.org › dictionary › english › standard-deviation
STANDARD DEVIATION | English meaning - Cambridge Dictionary
3 weeks ago - a number that shows the amount by which members of a group are different from the mean (= average) value for the group: Price dispersion in the region is measured by the standard deviation of prices for a product across the six economies.
Math is Fun
mathsisfun.com › data › standard-deviation.html
Standard Deviation and Variance
Deviation just means how far from the normal. The Standard Deviation is a measure of how spreadout numbers are.
Dummies
dummies.com › article › academics-the-arts › math › statistics › how-to-interpret-standard-deviation-in-a-statistical-data-set-169772
How to Interpret Standard Deviation in a Statistical Data Set | dummies
July 2, 2025 - Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean (or average) of the data set, and a large standard deviation means that the values in the data set are farther away from the mean.
ScienceDirect
sciencedirect.com › topics › mathematics › standard-deviation
Standard Deviation - an overview | ScienceDirect Topics
If we take the square root of the variance, the resulting number is called the standard deviation. The standard deviation is used to create bounds around the mean that describe data positions that are ± 1, ± 2, or ± 3 standard deviations from the mean.
Scribbr
scribbr.com › home › how to calculate standard deviation (guide) | calculator & examples
How to Calculate Standard Deviation (Guide) | Calculator & Examples
March 28, 2024 - The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean.
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
The standard deviation is used in conjunction with the mean to summarise continuous data, not categorical data.
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
Merriam-Webster
merriam-webster.com › dictionary › standard deviation
STANDARD DEVIATION Definition & Meaning - Merriam-Webster
3 weeks ago - The meaning of STANDARD DEVIATION is a measure of the dispersion of a frequency distribution that is the square root of the arithmetic mean of the squares of the deviation of each of the class frequencies from the arithmetic mean of the frequency distribution...
Statistics How To
statisticshowto.com › home › probability and statistics topics index › standard deviation: definition, examples
Standard Deviation: Simple Definition, Step by Step Video
June 26, 2025 - Standard deviation (SD) is a measure of the amount of variation in a set of values. A low SD—close to zero—indicates that the values tend to be close to the mean of the set, while a high SD indicates that the values are spread out over a ...
Statistics By Jim
statisticsbyjim.com › home › blog › standard deviation: interpretations and calculations
Standard Deviation: Interpretations and Calculations - Statistics By Jim
September 24, 2025 - The standard deviation (SD) is a single number that summarizes the variability in a dataset. It represents the typical distance between each data point and the mean. Smaller values indicate that the data points cluster closer to the mean—the ...
JMP
jmp.com › en › statistics-knowledge-portal › measures-of-central-tendency-and-variability › standard-deviation
Standard Deviation
The standard deviation measures the spread of a set of data values. A high standard deviation indicates a wide spread of data values, while a low standard deviation indicates a narrow spread of values clustered around the mean of the data set.
BYJUS
byjus.com › maths › standard-deviation
What are the Variance and Standard Deviation?
August 24, 2022 - Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean.
LeanScape
leanscape.io › home › lean wiki › demystifying standard deviation: a beginner’s guide
Demystifying Standard Deviation: A Beginner's Guide - LeanScape
Standard deviations describe the degree of dispersion of data in an area. The standard deviation returns a calculated amount to describe where the information is found. Normal distributions indicate the deviation between values from the mean.
Published September 23, 2024
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 ...