A = P e^{rt}, where P is principal, r is rate, t is time. Key Concepts Concept: Continuous compounding Concept: Exponential growth factor Concept: Final amount A Steps Action: Identify P, r, t Action: Use A = P e^{rt} Action: Interpret A as the future value Formula $$A = P e^{rt}$$
Mean Absolute Deviation (MAD) is the average distance from a center (mean or median). Key Concepts Concept: Center: mean x̄ or median x̃ Concept: Deviation: absolute value |x_i − center| Concept: MAD interpretation: average spread around center Steps Action: Choose center (mean or median) Action: Compute |x_i − center| for each data point Action: Average […]
Absolute deviation from a central value c is |x − c|. To find the Mean Absolute Deviation (MAD): $$text{MAD} = frac{1}{n} sum_{i=1}^{n} |x_i – bar{x}|.$$
Mean deviation (mean absolute deviation) is the average of the absolute differences from the data’s mean. Standard deviation measures data spread as the square root of the average squared deviations from the mean (population: divide by N; sample: divide by n−1).
Mean deviation about the mean = (1/n) Σ|x_i − x̄|. Key Concepts Concept: Definition of mean deviation Concept: Use of the sample mean overline{x} Concept: Population vs. sample versions Steps Action: Compute the mean overline{x} Action: Find absolute deviations |x_i − overline{x}| Action: Average deviations: (1/n) ∑ |x_i − overline{x}| Formula $$overline{D} = frac{1}{n} sum_{i=1}^{n} […]
Standard deviation measures how spread out data are around the mean; mean deviation (mean absolute deviation) is the average of the absolute differences from the mean.
MAD about the mean: MAD = (1/n) ∑_{i=1}^{n} |x_i – bar{x}|. Key Concepts Concept: Mean absolute deviation (MAD) Concept: Central value: mean or median Concept: Interpretation: average distance from center Steps Action: Compute the mean bar{x}. Action: Compute |x_i – bar{x}| for each i. Action: Sum deviations and divide by n. Formula $$text{MAD}_{text{mean}} = frac{1}{n} […]
Mean is the average of a data set. Standard deviation measures how spread out the data are around the mean.
Standard deviation measures how spread out a data set is; it is the square root of the variance.
Absolute deviation is the distance between a data point and a reference value, measured by the absolute value of their difference (e.g., |x − μ| or |x − M|, where μ is the mean or M is the median).
Deviation is the difference between an observed value and a reference value (such as the mean or target).
Please provide the expressions so I can identify their equivalent forms.
A fair game in probability has zero expected value; neither side has an edge.
The question is incomplete—please specify what the game requires (e.g., strategy, speed, or luck).
Examples of fair games include a coin toss (unbiased coin), dice-based games using a fair die, and rock–paper–scissors with equal chances for all players.
A game is fair if all players have an equal chance of winning under the stated rules.
I can’t determine the division expression without the model image or description. Please share the model or context.