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math: clarify data transformations

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eggy 2020-09-27 18:23:59 -04:00
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@ -196,11 +196,15 @@ In a typical bell-shaped distribution:
!!! info !!! info
The **points of inflection** (when the curve changes direction) of a normal bell curve occur at $\bar{x} ± \sigma$. The **points of inflection** (when the curve changes direction) of a normal bell curve occur at $\bar{x} ± \sigma$.
### Constant operations on mean and standard deviation ### Data transformation
When adding or subtracting a constant to a whole data set, the mean is increased/decreased by that constant, but the standard deviation **does not change**. When performing an operation with a constant value to a whole data set:
| Operation | Effect on mean | Effect on standard deviation |
| --- | --- | --- |
| Addition/Subtraction | Increased/decreased by constant | No change |
| Multiplication/Division | Multiplied/divided by constant | Multiplied/divided by constant |
When multiplying or dividing a constant to a whole data set, both the mean and the standard deviation are multiplied or divided by that constant, respectively.
### Linear correlation and regression ### Linear correlation and regression