Search Results

Percentage Change

\% \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Increase or decrease of a value as a percentage.

Average (Mean)

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

Add all values and divide by how many there are.

Place Value

N = \sum d_i \times 10^{i}

Each digit’s value depends on its position.

Percent Increase

new = old(1 + p)

Value after a percentage increase.

Percent Decrease

new = old(1 - p)

Value after a percentage decrease.

Square Root

\sqrt{n}

The value that squares to n.

AlgebraBasic

Absolute Value

|x| = \begin{cases} x & x \ge 0 \\ -x & x < 0 \end{cases}

Distance of a number from zero, always non-negative.

AlgebraBasic

Absolute Value Property

|ab| = |a|\,|b|

The absolute value of a product equals the product of absolute values.

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.

Median

M = \text{middle value of ordered data}

The middle value separating the higher and lower halves.

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.

Mode

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

The value that appears most often in a data set.

Range

R = x_{max} - x_{min}

The difference between the largest and smallest values.

Geometric Mean

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

The nth root of the product of n values.

Range

R = x_{max} - x_{min}

Difference between the largest and smallest values.

Statistics & ProbabilityAdvanced

Percentile Rank

PR = \frac{\text{below}}{n}\times 100

Percentage of values below a given score.

Z-Test Statistic

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

Tests whether a sample mean differs from a hypothesized value.

Mode

\text{most frequent value}

The value that appears most often in a data set.

Probability & CombinatoricsIntermediate

Weighted Mean

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

Average where values carry different weights.

Expected Value

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

Long-run average value of a random variable.

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.

Linear AlgebraAdvanced

Eigenvalue Equation

A\vec{v} = \lambda\vec{v}

Defines eigenvalues and eigenvectors of a matrix.

Electronics & CircuitsIntermediate

RMS Voltage

V_{rms} = \frac{V_{peak}}{\sqrt{2}}

Effective value of a sinusoidal voltage.

Nutrition & FoodBasic

Percent Daily Value (%DV)

\%DV = \frac{a}{r} \times 100

How much a nutrient in a serving contributes to daily needs.

Finance & InterestBasic

Compound Interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Value of principal compounded n times per year.

Continuous Compounding

A = P e^{rt}

Value with interest compounded continuously.

Finance & InterestBasic

Future Value

FV = PV(1 + r)^n

Future worth of a present sum.

Finance & InterestBasic

Present Value

PV = \frac{FV}{(1 + r)^n}

Present worth of a future sum.

Future Value of Annuity

FV = P\frac{(1+r)^n - 1}{r}

Future value of regular equal payments.

Present Value of Annuity

PV = P\frac{1 - (1+r)^{-n}}{r}

Present value of a series of equal payments.

Net Present Value

NPV = \sum_{t=0}^{n}\frac{C_t}{(1+r)^t}

Present value of a stream of cash flows.

Business & CommerceIntermediate

Perpetuity

PV = \frac{C}{r}

Present value of an infinite constant cash flow.

AccountingAdvanced

Double-Declining Balance

D = \dfrac{2}{n}\times Book\ Value

An accelerated depreciation method charging more expense in an asset’s early years.

AccountingAdvanced

Book Value per Share

BVPS = \dfrac{Equity - Preferred}{Shares\ Outstanding}

The net asset value backing each common share.

AccountingBasic

Book Value

BV = Cost - \text{Accumulated Depreciation}

Asset value on the balance sheet.

Customer Lifetime Value (CLV)

CLV = \dfrac{ARPU \times Gross\ Margin}{Churn\ Rate}

The total profit expected from a customer over the whole relationship.

EconomicsBasic

Opportunity Cost

OC = \frac{\text{what you give up}}{\text{what you gain}}

Value of the next best alternative foregone.

Currency & ForexIntermediate

Pip Value

Pip\ Value = \dfrac{Pip\ Size}{Rate}\times Lot

The monetary value of a one-pip move for a given trade size.

Everyday MathBasic

Unit Price

\text{Unit Price} = \frac{\text{Total Price}}{\text{Quantity}}

Price per single unit to compare value between products.

Everyday MathBasic

Percentage Change

\%\Delta = \frac{new - old}{old}\times 100

Relative change between two values.

Computer ScienceBasic

Bits to Represent n

b = \lceil \log_2(n) \rceil

Minimum number of bits to represent n distinct values.

Math Tricks (5)

Duplex Method for Squaring

The Dwandwa (duplex) method squares any number by summing duplex values digit by digit — a general Vedic squaring technique.

Add Left to Right

Add the big place values first (left to right) instead of the traditional right-to-left carrying — easier to hold in your head.

Product of Numbers Around a Square

Two numbers equally spaced around a middle value m multiply to m² − d², using the difference of squares.

Quick Celsius ↔ Fahrenheit

A fast approximation: to go C→F, double and add 30. For exact values use ×9/5 + 32.

Compare Unit Prices

To find the better deal, divide price by quantity to get the price per unit and compare.