How to Calculate Standard Deviation and Variance

Squaring ensures that negative differences don't cancel out positive ones. It also gives more weight to extreme outliers, making them easier to identify. If we simply used absolute differences, the math would be less robust for complex statistical modeling.

There is no universal "good" number; it depends on context. In a medical test, you want a very low standard deviation (high precision). In stock market returns, a high standard deviation indicates high volatility and risk.

Yes. Because it is the square root of variance (which is a sum of squared numbers), it will always be zero or a positive number. A standard deviation of zero means all data points are identical.

Standard deviation measures the spread of individual data points in a single sample. Standard error measures how far the sample mean is likely to be from the true population mean.

Use N-1 (Sample Statistics) when you are using a small group of data to make inferences about a larger population. Use N (Population Statistics) when you have recorded every single data point in the entire group you are studying.

Yes. If the variance is between 0 and 1, the square root (standard deviation) will be larger than the variance. For example, if variance = 0.25, then standard deviation = 0.5.

This is an alternative to standard deviation that uses absolute values instead of squaring. While simpler, it is less common because standard deviation has superior mathematical properties for probability theory.