Standard Deviation Calculator
Calculate mean, variance, and standard deviation (population and sample) of a dataset.
Statistics is the art of telling a story with data, and Standard Deviation is one of its most critical chapters. It measures amount of variation or dispersion in a set of values. 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 the values are spread out over a wider range. Our calculator instantly processes large datasets to compute the Mean, Population SD, and Sample SD.
Data Input
Frequently Asked Questions
Understanding the Bell Curve
Standard Deviation (SD) in statistics reveals the "story" behind an average. Two classes could both have an average test score of 80%, but one class might have everyone scoring between 75-85 (Low SD), while the other has half the class failing and half getting 100s (High SD). Variations in data matter just as much as the average.
1. The 68-95-99.7 Rule
For data that follows a normal distribution (the classic Bell Curve):
- 68% of data falls within 1 Standard Deviation of the mean.
- 95% of data falls within 2 Standard Deviations.
- 99.7% of data falls within 3 Standard Deviations.
2. Population vs. Sample SD
Population SD (σ): Use this when you have data for every single member of a group. For example, if you are measuring the height of every player on a specific football team, you have the entire population.
Sample SD (s): Use this when you only have a subset of data representing a larger group. If you survey 100 people to estimate the height of all adults in the US, you are using a sample. The formula divides by n-1 (Bessel's Correction) to create a slightly larger deviation, effectively penalizing you for not having all the data.
3. Frequently Asked Questions (FAQ)
Q: What is Variance?
Variance is simply the Standard Deviation squared. It is useful for mathematical proofs but less useful for describing real-world data because the units are squared (e.g., "squared dollars" vs "dollars").
Q: What is a "Z-Score"?
A Z-Score tells you how many standard deviations a specific data point is away from the mean. It helps you understand if a specific result is "normal" or an "outlier."