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 ...
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.
ELI5: someone please explain Standard Deviation to me.
I’ll give my shot at it: Let’s say you are 5 years old and your father is 30. The average between you two is 35/2 =17.5. Now let’s say your two cousins are 17 and 18. The average between them is also 17.5. As you can see, the average alone doesn’t tell you much about the actual numbers. Enter standard deviation. Your cousins have a 0.5 standard deviation while you and your father have 12.5. The standard deviation tells you how close are the values to the average. The lower the standard deviation, the less spread around are the values. More on reddit.com
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March 28, 2021ELI5: Standard deviation
The standard deviation basically gives you an idea of how far apart all the different measurements in a set are. When you have a set of numbers, the average (called the mean) equals all the numbers added up, then divided by the amount of numbers. The standard deviation tells describes the average distance of the measurements from the mean. The average distance to the average value. The bigger the difference, the larger the standard deviation. This tells you something about thing that you're measuring. Let's say you're tracking the scores of your classmates on the latest English exam. If the average (mean) is 6.7, and the standard deviation is 0.3, it means that your classmates, on average, scored pretty close to that grade. If the standard deviation is 2.9, it means that your classmates' scores were all over the place, some scoring very high, some scoring very low. Very simple example: take these 5 numbers: 3 9 7 4 2. Mean: 5 Std. deviation: 2.6 (rounded down). This means that the average 'distance' from the average (5) is 2.6 (either up or down). Edit: clarification More on reddit.com
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April 29, 2016ELI5: 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, 2016ELI5: What exactly does "1 standard deviation" mean when trying to interpret data?
The standard deviation is a measure of how spread out the data is. A dataset with a low standard deviation will have values tightly clustered around the mean, while a large standard deviation means there is a large variation between values. A standard deviation of 0 means every data point is equal. The standard deviation is found by taking the mean of the squared distances between each data point and the mean, and then taking the square root of that. For example, if you have the values 1,2,3,4,5, then: The mean is (1+2+3+4+5)/5=3 The differences between each data point and the mean are -2,-1,0,1,2 The squares of those differences are 4,1,0,1,4 The mean of those is 2 So the standard deviation is sqrt(2) or about 1.41 More on reddit.com
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October 26, 2016Videos
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
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.
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.
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 ...
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.
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
Calculator.net
calculator.net › home › math › standard deviation calculator
Standard Deviation Calculator
Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected ...
Statistics LibreTexts
stats.libretexts.org › bookshelves › introductory statistics › statistics: open for everyone (peter) › 4: measures of variability
4.3: Standard Deviation - Statistics LibreTexts
October 22, 2024 - This brings us to a measure of variability called the standard deviation. A standard deviation is a descriptive statistic that summarizes how far raw scores tended to fall from the mean in standard units.
Cambridge Dictionary
dictionary.cambridge.org › us › dictionary › english › standard-deviation
STANDARD DEVIATION definition | Cambridge English Dictionary
1 week 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.
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
Scribbr
scribbr.com › home › what does standard deviation tell you?
What does standard deviation tell you?
September 30, 2022 - 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
ScienceDirect
sciencedirect.com › topics › mathematics › standard-deviation
Standard Deviation - an overview | ScienceDirect Topics
Standard deviation is defined as the square root of variance, which measures the average squared differences from individual values to their mean, thereby providing a statistic that is at the same numeric scale as the data values.
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.
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 ...
W3Schools
w3schools.com › datascience › ds_stat_std.asp
Data Science Statistics Standard Deviation
A high standard deviation means that the values are spread out over a wider range.
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.
Dummies
dummies.com › article › academics-the-arts › math › statistics › standard-deviation-and-variance-147351
Standard Deviation and Variance | dummies
July 3, 2025 - A standard deviation measures the amount of variability among the numbers in a data set. It calculates the typical distance of a data point from the mean of the data. If the standard deviation is relatively large, it means the data is quite ...