Standard deviation measures the typical distance of observations from their mean. It summarizes variability in the same units as the underlying data, making spread easier to interpret than variance. section 14.1.3 section 12.5.3
Use the appropriate interpretation and calculation for the data and decision:
- For continuous measurements, calculate the square root of the average squared differences between observations and their mean. section 14.1.3
- For proportions in a p-chart, use the proportion of defectives, its complement, and the sample size; larger samples reduce proportion variability. section 14.1.3
- Interpret a larger value as greater spread or volatility, but compare values within the same measurement context. section 9.5.4 section 9.5.2
From historical returns to simulation
For GM daily log returns, Python calculates a mean of approximately −0.00061 and a standard deviation of 0.02005. The mean represents the average daily trend, while the standard deviation supplies the volatility parameter for generating simulated returns and potential future price paths. section 9.5.4
>>> mu = log_returns.mean() >>> print(mu) -0.000605520424324896 >>> sigma = log_returns.std() >>> print(sigma) 0.020045660849343817
Inspect the concise Python calculation of the mean and standard deviation used as Monte Carlo inputs. section 9.5.4
In quality control, an s-chart tracks sample standard deviations over time. Their average forms the center line, while correction-factor-based control limits identify unusually high or low process variability. section 14.3.3
