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Variance

\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2

Average squared deviation from the mean.

Z-Score

z = \frac{x - \mu}{\sigma}

Number of standard deviations a value is from the mean.

Expected Value

E[X] = \sum_i x_i\,p_i

The long-run average value of a random variable.

Standard Error of the Mean

SE = \frac{\sigma}{\sqrt{n}}

Standard deviation of the sample mean.

Geometric Mean

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n values.

Coefficient of Variation

CV = \frac{\sigma}{\bar{x}}\times 100\%

Relative variability as a percentage of the mean.

Coefficient of Variation

CV = \frac{\sigma}{\mu}\times 100

Relative variability as a percentage of the mean.

Margin of Error

E = z\frac{\sigma}{\sqrt{n}}

Half-width of a confidence interval for the mean.

Confidence Interval (Mean)

\bar{x} \pm z\frac{\sigma}{\sqrt{n}}

Range likely to contain the population mean.

Z-Test Statistic

z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}

Tests whether a sample mean differs from a hypothesized value.

Probability & CombinatoricsIntermediate

Weighted Mean

\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}

Average where values carry different weights.

Variance of a Random Variable

Var(X) = E[X^2] - (E[X])^2

Measures the spread of a random variable around its mean.

Mean Squared Error (MSE)

MSE = \frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2

Average of squared differences between predicted and actual values.

Root Mean Squared Error (RMSE)

RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}

Square root of MSE, in the same units as the target variable.

Data Science & MLIntermediate

Mean Absolute Error (MAE)

MAE = \frac{1}{n}\sum_{i=1}^{n}|y_i - \hat{y}_i|

Average of absolute differences between predictions and actual values.

F1 Score

F_1 = 2\cdot\frac{Precision \cdot Recall}{Precision + Recall}

Harmonic mean of precision and recall.