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16 results for “range”

Formulae (16)

Permutations

P(n,r) = \frac{n!}{(n-r)!}

Number of ordered arrangements of r items from n.

Statistics & ProbabilityBasic

Range

R = x_{max} - x_{min}

The difference between the largest and smallest values.

Statistics & ProbabilityIntermediate

Interquartile Range

IQR = Q_3 - Q_1

The spread of the middle 50% of the data.

Statistics & ProbabilityBasic

Range

R = x_{max} - x_{min}

Difference between the largest and smallest values.

Statistics & ProbabilityIntermediate

Interquartile Range

IQR = Q_3 - Q_1

Spread of the middle 50% of the data.

Statistics & ProbabilityAdvanced

Confidence Interval (Mean)

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

Range likely to contain the population mean.

Probability & CombinatoricsBasic

Permutations

P(n,r) = \frac{n!}{(n-r)!}

Number of ordered arrangements of r items from n.

Probability & CombinatoricsBasic

Permutations with Repetition

n^r

Ordered arrangements of r items from n when repetition is allowed.

Probability & CombinatoricsIntermediate

Permutations of a Multiset

\frac{n!}{n_1! n_2! \cdots n_k!}

Arrangements of n items where some are identical.

Data Science & MLIntermediate

Sigmoid Function

\sigma(x) = \frac{1}{1 + e^{-x}}

Maps any real number to the range (0, 1); used in logistic regression.

Data Science & MLBasic

Min-Max Normalization

x' = \frac{x - x_{min}}{x_{max} - x_{min}}

Rescales features to the range [0, 1].

PhysicsIntermediate

Projectile Range

R = \frac{v^2\sin 2\theta}{g}

Horizontal distance of a projectile on level ground.

Health & FitnessIntermediate

Heart Rate Reserve

HRR = HR_{max} - HR_{rest}

The usable range between rest and maximum heart rate.

Aviation & AeronauticsIntermediate

Specific Range

SR = \dfrac{GS}{\dot{f}}

Distance flown per unit of fuel; maximizing it gives best fuel economy.

Aviation & AeronauticsAdvanced

Breguet Range Equation

R = \dfrac{V}{c}\dfrac{L}{D}\ln\dfrac{W_i}{W_f}

Maximum range of a jet aircraft from speed, efficiency, L/D and fuel fraction.

Aviation & AeronauticsAdvanced

Great Circle Distance

d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Shortest distance between two points on the Earth for long-range navigation.