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Standard Deviation Calculator
What Does Standard Deviation Actually Mean?
In plain English? It measures how "spread out" your numbers are. That's it.
- Low SD: Everyone got a 'B' on the test. The scores are bunched together.
- High SD: Some got 'A's, some failed. The scores are all over the place.
💡 Real Talk from Dr. Alex M., Ph.D.
The biggest confusion I see? Population vs. Sample. If you're doing homework, 90% of the time you want Sample Standard Deviation (divide by N-1). Why? Because you rarely have data for the entire population. If you're unsure, ask your teacher, but Sample SD is the safer bet.
Variance vs. Standard Deviation
Variance is just the Standard Deviation squared. But here's the problem: Variance is in "squared units."
Example: If you measure height in inches, Variance is in "square inches." What does a square inch of height mean? Nothing. That's why we take the square root to get Standard Deviation, which brings us back to plain old "inches."
⚠️ Common Mistake: Dividing by N instead of N-1
This is the classic rookie mistake.
• Population (N): You have data for every single person/item.
• Sample (N-1): You have a sample representing a larger group.
Using N-1 makes the result slightly larger, which accounts for the uncertainty of using a
sample. It's called "Bessel's Correction."
Reviewed by Dr. Alex M., Ph.D.
Mathematics Professor
Last updated: November 2025
Frequently Asked Questions
What does Standard Deviation actually mean?
Think of it as the 'spread' of your data. Low SD means all the numbers are close to the average (consistent). High SD means they're all over the place (volatile). If you're grading a class, low SD means everyone got similar scores. High SD means some failed and some aced it.
Should I use Population or Sample SD?
If you have data for EVERYONE (like the entire class), use Population SD (divide by N). If you only have a small group representing a larger one (like a survey of 100 people out of 1000), use Sample SD (divide by N-1). When in doubt for homework, it's usually Sample SD.
Why do we square the differences?
To get rid of negative numbers. If we just added up the differences from the mean, the negatives and positives would cancel out to zero. Squaring makes everything positive so we can measure the total distance.
What is Variance?
Variance is just Standard Deviation squared. It's useful for math proofs, but Standard Deviation is more useful for real life because it's in the same units as your data (e.g., dollars or inches, not 'dollars squared').
What is the 68-95-99.7 rule?
For a normal distribution (bell curve): 68% of data falls within 1 SD of the mean. 95% falls within 2 SDs. 99.7% falls within 3 SDs. If you're outside 3 SDs, you're an outlier (a weirdo, statistically speaking).