10. Variance and Standard Deviation
Variance and standard deviation are fundamental statistical measures that indicate how much the values in a dataset deviate from the mean. Variance measures the average squared deviation from the mean, while standard deviation is the square root of variance, providing a more interpretable measure of dispersion. Both concepts are crucial in engineering, particularly in analyzing data, modeling uncertainty, and solving partial differential equations (PDEs).
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What we have learnt
- Variance measures the average squared deviation from the mean.
- Standard deviation is the square root of variance and is used for easier interpretation.
- Both variance and standard deviation are essential in analyzing engineering data and modeling systems under uncertainty.
Key Concepts
- -- Mean (Average)
- The mean is calculated by summing all data points and dividing by the number of points, providing a measure of central tendency.
- -- Variance
- Variance quantifies the spread of data points from their mean and is calculated as the average of the squared differences.
- -- Standard Deviation
- Standard deviation is a measure of dispersion that is the square root of variance, providing insights in the same units as the original data.
- -- Properties of Variance and SD
- Both variance and standard deviation are non-negative, affected by outliers, exhibit additive properties for independent variables, and have scaling rules.
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