What is the difference between population and sample standard deviation?

Q: What is standard deviation?

Standard deviation measures how spread out data is from the average (mean). A low standard deviation means data points are close to the mean; a high standard deviation means they're spread over a wider range. It's the most common measure of statistical dispersion and is expressed in the same units as the data.

Q: What's the difference between population and sample standard deviation?

Population standard deviation (σ) divides by N (total data points) when you have data for the entire population. Sample standard deviation (s) divides by N-1 (Bessel's correction) when working with a sample to estimate the population parameter. Using N-1 provides an unbiased estimate.

Q: What is variance and how does it relate to standard deviation?

Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance. While variance is in squared units (hard to interpret), standard deviation is in the original units (easy to interpret). SD = √Variance. Both measure spread, but SD is more intuitive.

Q: What does a standard deviation of 1 mean?

By itself, it depends on context. In a normal distribution, about 68% of data falls within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD (the 68-95-99.7 rule). If the mean is 100 and SD is 1, then 68% of data falls between 99 and 101.

Q: When should I use standard deviation vs other measures of spread?

Use standard deviation for normally distributed data and when the mean is a good measure of center. For skewed data or data with outliers, consider IQR (interquartile range) or MAD (median absolute deviation). Standard deviation is sensitive to outliers, which can inflate the result significantly.

Question

What is the difference between population and sample standard deviation?

Accepted Answer

Population SD divides by N (all data points). Sample SD divides by N-1 (Bessel correction) and is used when your data is a sample of a larger population.

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