expectation of the squared deviation of a random variable from its mean
Wikipedia
en.wikipedia.org › wiki › Variance
Variance - Wikipedia
5 days ago - In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are ...
CalculatorSoup
calculatorsoup.com › calculators › statistics › variance-calculator.php
Variance Calculator
November 4, 2025 - Calculate the variance. Variance is the sum of squares divided by the number of data points. ... The formula for variance of a is the sum of the squared differences between each data point and the mean, divided by the number of data values.
[Q] What is variance?
Variance isn't specific to bell curves. For instance, Gaussian mixtures can have wildly different multimodal PDFs that look nothing like bell curves, but they have finite variance anyway. The exponential distribution doesn't look like a bell curve either but it has a finite variance. For a normal distribution (the ultimate bell curve), "the theoretical span of the bell curve's end" doesn't make sense to me because there's no end as the support of the normal distribution is the entirety of real numbers. Both tails go to infinity. Variance measures the average squared distance between realizations of a random variable and its mean. Or, it measures the average/expected deviation from the mean. Or, it's the average squared error you'll make when guessing that the value of the random variable is actually constant and equal to its expected value. In general, variance is one measure of variability if your data or your distribution. Indeed, other measures of variability exist, like (interquartile) range or mean absolute deviation. More on reddit.com
48
2
April 11, 2024[Statistics] variance formula for binomial distribution
I have to ask though, what is "/(1-n)" That should be (N-1), according to Wikipedia , assuming that p = K/N. More on reddit.com
3
1
January 14, 2016Formula for variance above a constantly changing mean
You might benefit from a simpler (A1-Avg(A1:A)) function If you can share an example of what you have and what you want I can be more specific More on reddit.com
7
5
February 20, 2020BEC Variance Analysis - Overhead Variance Formula
Seen a lot of people struggle with this concept. Here is what helped me: https://m.youtube.com/watch?feature=player_embedded&v=zt2X6OOXBdc More on reddit.com
4
5
May 10, 2020What is variance used for in statistics?
Statistical tests such as variance tests or the analysis of variance (ANOVA) use sample variance to assess group differences of populations. They use the variances of the samples to assess whether the populations they come from significantly differ from each other.
scribbr.com
scribbr.com › home › how to calculate variance | calculator, analysis & examples
How to Calculate Variance | Calculator, Analysis & 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 variance | calculator, analysis & examples
How to Calculate Variance | Calculator, Analysis & Examples
What are the 4 main measures of variability?
Variability is most commonly measured with the following descriptive statistics: · Range: the difference between the highest and lowest values · Interquartile range: the range of the middle half of a distribution · Standard deviation: average distance from the mean · Variance: average of squared distances from the mean
scribbr.com
scribbr.com › home › how to calculate variance | calculator, analysis & examples
How to Calculate Variance | Calculator, Analysis & Examples
Videos
05:47
How to Calculate Variance and Standard Deviation - YouTube
00:41
Variance and standard deviation in 40 seconds - YouTube
Statistics: Alternate variance formulas (video)
Variance of a population (video)
16:35
Understanding Population and Sample Variance - YouTube
DLsun
dlsun.github.io › probability › variance.html
Lesson 28 Variance | Introduction to Probability
Now, if we know that a random variable \(X\) has a binomial distribution, we can use the formula \[ \text{Var}[X] = n\frac{N_1}{N} \frac{N_0}{N} \] instead of calculating it from scratch. We can derive formulas for the variances of all of the named distributions in a similar way.
Scribbr
scribbr.com › home › how to calculate variance | calculator, analysis & examples
How to Calculate Variance | Calculator, Analysis & Examples
June 21, 2023 - When you collect data from a sample, the sample variance is used to make estimates or inferences about the population variance. ... With samples, we use n – 1 in the formula because using n would give us a biased estimate that consistently underestimates variability.
Probability Course
probabilitycourse.com › chapter3 › 3_2_4_variance.php
Variance | Standard Deviation
By definition, the variance of $X$ is the average value of $(X-\mu_X)^2$. Since $(X-\mu_X)^2 \geq 0$, the variance is always larger than or equal to zero. A large value of the variance means that $(X-\mu_X)^2$ is often large, so $X$ often takes values far from its mean.
Loughborough University
lboro.ac.uk › media › media › schoolanddepartments › mlsc › downloads › var_stand_deviat_group.pdf pdf
Variance and standard deviation (grouped data) Introduction
The variance of a set of values, which we denote by σ2, is defined as · σ2 = f(x −¯x)2 · n · where ¯x is the mean, x stands for each data value in turn, and f is the frequency with which data · value, x, occurs. Note that · f = n. An alternative, yet equivalent formula, which ...
Math is Fun
mathsisfun.com › data › standard-deviation.html
Standard Deviation and Variance
The formula is easy: it is the square root of the Variance.
GeeksforGeeks
geeksforgeeks.org › mathematics › variance
Variance | Definition, Formula, Examples & Properties - GeeksforGeeks
November 4, 2025 - In general, variance means population standard variance. The steps to calculate the variance of a given set of values are, Step 1: Calculate the mean of the observation using the formula (Mean = Sum of Observations/Number of Observations)
Corporate Finance Institute
corporatefinanceinstitute.com › home › resources › variance formula
Variance Formula - Calculate, Free Templates, Types
June 10, 2025 - This is an example of outperformance, a positive variance, or a favorable variance. The formula for dollar variance is even simpler. It’s equal to the actual result subtracted from the forecast number. If the units are dollars, this gives us the dollar variance.
Penn State Statistics
online.stat.psu.edu › stat504 › lesson › variance
Variance | STAT 504
That is, V (X) is the average squared distance between X and its mean. Variance is a measure of dispersion, telling us how “spread out” a distribution is.
BYJUS
byjus.com › variance-formula
Variance Formulas for Grouped Data
November 22, 2021 - In probability theory and statistics, the variance formula measures how far a set of numbers are spread out. It is a numerical value and is used to indicate how widely individuals in a group vary.
Vintti
vintti.com › blog › variance-analysis-formula-accounting-explained
Variance Analysis Formula: Accounting Explained — Vintti
Expense Variance = Budgeted Expense - Actual Expense · These formulas allow you to analyze the difference between your actual financial results and what was budgeted.
Outlier
articles.outlier.org › how-to-calculate-variance
How To Calculate Variance In 4 Simple Steps | Outlier
March 23, 2022 - Your data should be included inside the parentheses, so if you have ten data points in cells A1 through A10; the formula would be =VAR(A1:A10). In Desmos and R, the command for variance is also VAR(). You can type your data right between the parentheses, so if your data consists of the set of numbers {5, 7, 10, 15, 20} you would type VAR(5, 7, 10, 15, 20).
Investopedia
investopedia.com › terms › v › variance.asp
What Is Variance in Statistics? Definition, Formula, and Example
June 18, 2025 - For instance, when calculating a sample variance to estimate a population variance, the denominator of the variance equation becomes N − 1 so that the estimation is unbiased and does not underestimate the population variance.
YouTube
youtube.com › the organic chemistry tutor
How To Calculate Variance - YouTube
This statistics video tutorial explains how to calculate the variance of a sample. How To Calculate Standard Deviation: https://www.youtube.com/watch?v=IaTFp...
Published May 20, 2020 Views 21K
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 - Variance is a measure of how far the observed values in a dataset fall from the arithmetic mean, and is therefore a measure of spread - more specifically, it is a measure of variability. It is denoted by the Greek letter sigma squared, and its formula is given by:
Hunter College
hunter.cuny.edu › dolciani › pdf_files › brushup-materials › calculating-variance-and-standard-deviation.pdf pdf
Calculating Variance and Standard Deviation
Skip to content. | Skip to navigation · About Mary P. Dolciani DMLC Mission
Statlect
statlect.com › fundamentals-of-probability › variance
Variance | Definition based on the expected value
Definition Let be a random variable. Denote the expected value operator by . The variance of is provided the expected values in the formula exist.
Reddit
reddit.com › r/statistics › [q] what is variance?
r/statistics on Reddit: [Q] What is variance?
April 11, 2024 -
A student asked me what does variance mean? "Why is the number so large?" she asked.
I think it means the theoretical span of the bell curve's ends. It is, after all, an alternative to range. Is that right?
Top answer 1 of 14
29
Variance isn't specific to bell curves. For instance, Gaussian mixtures can have wildly different multimodal PDFs that look nothing like bell curves, but they have finite variance anyway. The exponential distribution doesn't look like a bell curve either but it has a finite variance. For a normal distribution (the ultimate bell curve), "the theoretical span of the bell curve's end" doesn't make sense to me because there's no end as the support of the normal distribution is the entirety of real numbers. Both tails go to infinity. Variance measures the average squared distance between realizations of a random variable and its mean. Or, it measures the average/expected deviation from the mean. Or, it's the average squared error you'll make when guessing that the value of the random variable is actually constant and equal to its expected value. In general, variance is one measure of variability if your data or your distribution. Indeed, other measures of variability exist, like (interquartile) range or mean absolute deviation.
2 of 14
14
I think it means the theoretical span of the bell curve's ends Not really. You seem to be confusing variance with standard deviation or some multiple of it, perhaps 4 or 6 standard deviations of width (2-3 each side of the mean)? On a normal distribution, the distance from the center to the part where the curve is dropping fastest - where it's almost a straight line - is one standard deviation (which is the square root of variance), but the ends of the normal distribution? Not really; the normal distribution covers the entire number line; it doesn't have ends as such. But most of the normal distribution is within 3 standard deviations of the mean. It would be misleading to focus too much on the normal distribution when discussing variance. Variance and standard deviation are defined for any distribution of a random variable (albeit they're not always finite). It is, after all, an alternative to range I think you may have just jumped from talking about distributions to samples; in a sample the range and the standard deviation (not variance) are both ways to measure scale. That is, they measure how widely "spread" the distribution is, in the same units as the original variable. The range can be okay as a sample measure of spread with samples from very light-tailed distributions; not usually of much value otherwise. There are many other measures of spread besides those two. But once we move from samples back to distributions, range* is of little value as a measure of spread** -- with many distributions the range is infinite. "Why is the number so large?" she asked. It's in squared units. If the numerical value of the standard deviation is large, variance will have a really large number attached to it. If the value of standard deviation is small (much less than 1), the variance will be really small. * more strictly, the bounds of the support of the random variable ** outside distributions with bounded support but there's relatively few in common use compared to distributions on the whole line or the half line.
Kellogg School of Management
kellogg.northwestern.edu › faculty › weber › decs-433 › Notes_4_Random_variability.pdf pdf
Random Variability
Then the total demand is D⋅LT, with expected value D⋅E[LT] and variance D2⋅Var[LT].