MAD is the average of the absolute deviations from the mean: $$mathrm{MAD} = frac{1}{n} sum_{i=1}^{n} left| x_i – bar{x} right|.$$
Mean deviation is the average of the absolute deviations from the mean. Standard deviation is the square root of the average of the squared deviations.
Mean deviation about the mean is the average of absolute deviations from the mean. Key Concepts Concept: Definition of MAD about mean Concept: Absolute deviations used Concept: Measures data dispersion Steps Action: Compute the mean Action: Compute |x_i – mean| for each value Action: Average the deviations: sum/n Formula $$text{MAD}_{text{mean}} = frac{1}{n} sum_{i=1}^{n} left| x_i […]
Standard deviation measures spread around the mean using squared deviations; mean deviation (MAD) uses average absolute deviations.
Mean deviation equals the average absolute deviation from the center. Key Concepts Concept: Mean absolute deviation Concept: Center: mean μ or x̄ Concept: Absolute deviations: |x_i − center| Steps Action: Choose center (mean μ or x̄) Action: Compute |x_i − center| for all i Action: Average: MD = (1/n) Σ |x_i − center| Formula $$text{MAD} […]
Standard deviation is a measure of how spread out the data are around the mean.
Absolute deviation is the distance between a value x and a central point c, measured as |x − c|. The mean absolute deviation (MAD) is the average of these absolute deviations: $$text{MAD} = frac{1}{n} sum_{i=1}^n |x_i – bar{x}|.$$
Deviation is the amount by which something differs from a standard, norm, or expected value.
This question needs more information to provide a complete answer. Missing Details Specify: The expressions to compare (please list them). Clarify: Do you want algebraic equivalents, trigonometric identities, or another type of equivalence? Provide: Any domain/constraints or required steps for the solution. Try Asking “Identify the equivalent expression for each of the expressions below: [list […]
A fair game in probability is one with zero expected value: on average, no player gains or loses, typically because all outcomes are equally likely.
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Examples of fair games include coin-flip challenges, rock–paper–scissors, dice-rolling games with equal odds, and card games played with a fair shuffle.
A game is fair if all players have equal chances of winning and the expected payoff for every player is zero (no one has an edge).
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A step-by-step algebra calculator solves algebraic equations and shows each solving step for you.
Continuous compounding yields A = P e^{rt}, with P principal, r rate, t time. Key Concepts Concept: Continuous compounding Concept: Differential equation dA/dt = r A Concept: Exponential growth function Steps Action: Assume constant r; set dA/dt = r A Action: Solve with A(0) = P Action: Conclude A(t) = P e^{rt} Formula $$A(t) = […]