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21 results for “metric”

Formulae (21)

Geometric Series Sum

S_n = a_1 \frac{1 - r^n}{1 - r}

Sum of the first n terms of a geometric sequence (r ≠ 1).

AlgebraIntermediate

Infinite Geometric Series

S = \frac{a_1}{1 - r}, \quad |r| < 1

Sum of an infinite geometric series that converges.

AlgebraIntermediate

Geometric Mean

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

The nth root of the product of n numbers.

AlgebraAdvanced

Infinite Geometric Series

S = \frac{a}{1-r}, \; |r|<1

Sum of an infinite geometric series that converges.

AlgebraIntermediate

Finite Geometric Series

S_n = a\frac{1-r^n}{1-r}

Sum of the first n terms of a geometric series.

Geometry & TrigonometryIntermediate

Pythagorean Identity

\sin^2\theta + \cos^2\theta = 1

The fundamental trigonometric identity.

Statistics & ProbabilityIntermediate

Geometric Mean

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

The nth root of the product of n values.

Probability & CombinatoricsIntermediate

Geometric Probability

P(X=k) = (1-p)^{k-1} p

Probability that the first success occurs on trial k.

Data Science & MLBasic

Classification Accuracy

Accuracy = \frac{TP + TN}{TP + TN + FP + FN}

Fraction of predictions that are correct.

Data Science & MLIntermediate

Precision

Precision = \frac{TP}{TP + FP}

Of all positive predictions, the fraction that were correct.

Data Science & MLIntermediate

Recall (Sensitivity)

Recall = \frac{TP}{TP + FN}

Of all actual positives, the fraction correctly identified.

Data Science & MLIntermediate

F1 Score

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

Harmonic mean of precision and recall.

Data Science & MLIntermediate

Specificity

Specificity = \frac{TN}{TN + FP}

Of all actual negatives, the fraction correctly identified.

Fluid MechanicsBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Nutrition & FoodIntermediate

Food Cost Percentage

FC = \frac{c_{ingredients}}{p_{selling}} \times 100

Ingredient cost as a share of menu price — a core restaurant metric.

EngineeringBasic

Volumetric Flow Rate

Q = Av

Volume of fluid passing per unit time.

Aviation & AeronauticsAdvanced

Barometric Altitude

h = \dfrac{RT}{g}\ln\dfrac{P_0}{P}

Altitude derived from the ratio of sea-level to measured pressure.

Business & CommerceAdvanced

Month-over-Month Growth

g = \left(\dfrac{V_1}{V_0}\right) - 1

The percentage change in a metric from one period to the next.

Geography & EarthAdvanced

Barometric Formula

P = P_0 e^{-\frac{Mgh}{RT}}

Atmospheric pressure as a function of altitude.

Geography & EarthAdvanced

Radiometric Dating Age

t = \frac{1}{\lambda}\ln\!\left(1 + \frac{D}{P}\right)

Age of a rock from parent and daughter isotopes.

Unit ConversionsBasic

Metric Tonnes to Pounds

\text{lb} = \text{t} \times 2204.62

Convert metric tonnes to pounds.