Variance measures how widely values spread around their mean. Calculate each deviation, square it, add the squares, and divide by the number of values. Taking the square root of variance produces standard deviation. section 1.5
For a pandas Series, the calculation follows this sequence:
- Subtract s.mean() from every value. section 1.5
- Square and sum the deviations, then divide by s.count() to obtain population variance. section 1.5
- Use the square root of that result as standard deviation; pandas' default standard-deviation calculation instead divides by count minus one. section 1.5
Match the population calculation
For a Series s, math.sqrt(((s - s.mean()) ** 2).sum() / s.count()) calculates the square root of population variance. In pandas, s.std(ddof=0) produces the same population standard deviation; the ddof choice explains why the default s.std() differs. section 1.5
