Mean computed first.
Sum of values divided by count. AskSia shows the arithmetic.
Step 1
AI Solver by AskSia
Variance Solver: the right formula for your data
Type or photograph your data values. AskSia computes the mean, then the squared deviations from the mean, then averages them (population) or divides by n minus 1 (sample) to get the variance. Standard deviation also reported.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is variance and how is it computed?
Variance measures the spread of a dataset around its mean. Population variance is the average of the squared deviations from the mean: sigma squared equals the sum of squared deviations divided by N, where N is the population size. Sample variance divides by n minus 1 instead of n to give an unbiased estimator. The standard deviation is the square root of the variance, giving spread in the original units.
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solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Variance.
Every step transparent, every answer self-checked.
Squared deviations.
Subtract mean from each value, square the result, tabulated for transparency.
Step 2
Population or sample.
Divide by N or n minus 1, depending on whether the data is full population or a sample.
Choice
Standard deviation too.
Square root of variance gives the standard deviation in original units.
SD
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Variance problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Variance solver covers.
Population variance.
Full census or fixed population. Divide by N.
Population
Sample variance.
Random sample from a larger population. Divide by n minus 1.
Sample
Standard deviation.
Square root of variance. Same units as the original data.
SD
Variance of distributions.
Expected value of (X minus mu) squared for discrete or continuous random variables.
Probability
Pooled variance.
Combine variances from two samples for a t-test setup.
Inference
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
Why divide by n minus 1 for the sample variance?
Dividing by n minus 1 (Bessel's correction) gives an unbiased estimator of the population variance. If you divided by n, the sample variance would systematically underestimate the true population variance because the sample mean is closer to the data than the population mean. The n minus 1 correction compensates for this bias.
What is the difference between variance and standard deviation?
Variance is the average squared deviation from the mean, so its units are squared. Standard deviation is the square root of variance, so its units match the original data. Standard deviation is more interpretable because it has the same units as the data. AskSia reports both.
How do I know whether to use population or sample variance?
Use population variance (divide by N) when your data covers the entire population of interest. Use sample variance (divide by n minus 1) when your data is a random sample from a larger population that you want to make inferences about. For most real-world statistics problems, sample variance is appropriate.
What is the variance of a probability distribution?
For a discrete random variable X, the variance equals the sum of (x minus mu) squared times P(x), where mu is the expected value. For a continuous random variable, it equals the integral of (x minus mu) squared times the density. These match the data-based definitions in the limit of large samples.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Mean, squared deviations, divide.
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