Interactive Management Science: The Flaw of Averages
Interactive Management Science
MS&E 107/207, Midterm Review
The Flaw of the Averages
Mindle 1 / Uncertainty vs. Risk * Risk is in the eye of the beholder * Risk reflects how uncertain outcomes cause loss or injury to a particular individual or group * Risk attitude measures the willigness to incur risk in the quest of reward * Different risks to the same uncertainty
Mindle 2 / An uncertain number is a shape * A distribution * “Uncertain numbers” * Risk is subjective * Give-me-a-number mentality * Management of uncertainty: “Commitment to trade short-term rewards for long-term gains” * Flat Shape * To display a distribution: a histogram * Other important shape: cumulative distribution; shows the probability that the number is less than a given value * The average, mean or expected value; of the uncertain number is the balance point of the distribution * The median; quantify that the uncertain number has a 50/50 change of being greater or less than * The mode is the place at which the histogram has its highest peak, the most likely
Mindle 3 / Combinations of uncertain numbers * A combination of uncertain numbers is a SHAPE that goes up in the middle * This effect arises from diversification (central limit theorem) * What enough independent uncertain numbers are added together, the resulting distribution becomes bell shaped * Normal Distribution -> Highest in the middle, slow in the extremes * Resampling
Standard Deviation = Sigma^2 = Variance
“The balance point of the graph is the average”
Mindle 4 / Jensen’s Inequality * “Average inputs don’t always yield outputs” *Unless the model is linear * Some times when you plug averages of uncertain values into your plans, its overestimates the average outcome, and sometimes it underestimates the average outcome.
Mindle 5 / Interrelated Uncertains * Diversification -> Reduce risk
Weak form of the Flaw of
MS&E 107/207, Midterm Review
The Flaw of the Averages
Mindle 1 / Uncertainty vs. Risk * Risk is in the eye of the beholder * Risk reflects how uncertain outcomes cause loss or injury to a particular individual or group * Risk attitude measures the willigness to incur risk in the quest of reward * Different risks to the same uncertainty
Mindle 2 / An uncertain number is a shape * A distribution * “Uncertain numbers” * Risk is subjective * Give-me-a-number mentality * Management of uncertainty: “Commitment to trade short-term rewards for long-term gains” * Flat Shape * To display a distribution: a histogram * Other important shape: cumulative distribution; shows the probability that the number is less than a given value * The average, mean or expected value; of the uncertain number is the balance point of the distribution * The median; quantify that the uncertain number has a 50/50 change of being greater or less than * The mode is the place at which the histogram has its highest peak, the most likely
Mindle 3 / Combinations of uncertain numbers * A combination of uncertain numbers is a SHAPE that goes up in the middle * This effect arises from diversification (central limit theorem) * What enough independent uncertain numbers are added together, the resulting distribution becomes bell shaped * Normal Distribution -> Highest in the middle, slow in the extremes * Resampling
Standard Deviation = Sigma^2 = Variance
“The balance point of the graph is the average”
Mindle 4 / Jensen’s Inequality * “Average inputs don’t always yield outputs” *Unless the model is linear * Some times when you plug averages of uncertain values into your plans, its overestimates the average outcome, and sometimes it underestimates the average outcome.
Mindle 5 / Interrelated Uncertains * Diversification -> Reduce risk
Weak form of the Flaw of