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27 results for “average”

Formulae (26)

Average (Mean)

\text{average} = \frac{\text{sum of values}}{\text{number of values}}

Add all values and divide by how many there are.

AlgebraIntermediate

Geometric Mean

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

The nth root of the product of n numbers.

AlgebraAdvanced

Harmonic Mean

HM = \frac{n}{\sum 1/x_i}

Reciprocal of the average of reciprocals.

CalculusAdvanced

Average Value of a Function

f_{avg} = \frac{1}{b-a}\int_a^b f(x)\,dx

The mean value of a continuous function over an interval.

CalculusAdvanced

Mean Value Theorem

f'(c) = \frac{f(b)-f(a)}{b-a}

Guarantees a point where the tangent equals the average slope.

CalculusAdvanced

Average Value of a Function

\bar{f} = \frac{1}{b-a}\int_a^b f(x)\,dx

Mean value of a continuous function over an interval.

Statistics & ProbabilityBasic

Arithmetic Mean

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

The average of a data set.

Statistics & ProbabilityIntermediate

Variance

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

Average squared deviation from the mean.

Statistics & ProbabilityIntermediate

Expected Value

E[X] = \sum_i x_i\,p_i

The long-run average value of a random variable.

Statistics & ProbabilityBasic

Mode

\text{Mode} = \text{most frequent value}

The value that appears most often in a data set.

Statistics & ProbabilityIntermediate

Geometric Mean

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

The nth root of the product of n values.

Statistics & ProbabilityIntermediate

Weighted Mean

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

Average where values carry different weights.

Probability & CombinatoricsIntermediate

Expected Value

E[X] = \sum_{i} x_i\, p_i

Long-run average value of a random variable.

Probability & CombinatoricsAdvanced

Poisson Probability

P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}

Probability of k events in a fixed interval given average rate λ.

Data Science & MLBasic

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.

Data Science & MLBasic

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.

Thermodynamics & HeatAdvanced

Average KE of a Gas Molecule

\bar{E} = \tfrac{3}{2}k_B T

Mean translational kinetic energy per molecule.

Electronics & CircuitsAdvanced

Drift Velocity

v_d = \frac{I}{nAq}

Average velocity of charge carriers.

Biology & Life SciencesAdvanced

Hemocytometer Cell Count

C = \bar{n} \times DF \times 10^4

Cells per mL from a counting-chamber average.

Health & FitnessIntermediate

Mean Arterial Pressure

MAP = DBP + \tfrac{1}{3}(SBP - DBP)

Average blood pressure during a cardiac cycle.

AccountingIntermediate

Inventory Turnover

IT = \dfrac{COGS}{Average\ Inventory}

How many times inventory is sold and replaced over a period.

Business & CommerceIntermediate

Customer Acquisition Cost (CAC)

CAC = \dfrac{Sales\ \&\ Marketing\ Cost}{New\ Customers}

The average cost to win one new customer.

EconomicsBasic

GDP per Capita

\frac{GDP}{Population}

Average economic output per person.

Everyday MathBasic

Average Speed

v = \frac{d}{t}

Distance covered per unit time.

Computer ScienceAdvanced

Shannon Entropy

H = -\sum_i p_i \log_2 p_i

Average information content of a random source (bits).

Computer ScienceAdvanced

Average Memory Access Time

AMAT = H + M \times P

Effective access time from hit time, miss rate, and penalty.

Math Tricks (1)

Estimate a Square Root

Bracket the number between two perfect squares, then refine with a quick average step.

View trick