# Midterm Review Essay

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

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An uncertain number can be thought of a shape, known as a histogram, which depicts the likelihood that the number will take on different values.

The intervals covered by the bars are called bins. The histogram can have any shape, as long as the bars total 100%. If you think of the bars as blocks of wood sitting on a board, then the average, also known as the mean or expected value of the uncertain number, is the point at which the board would balance.

The more trials you run and the more bins you add, the greater the accuracy of the picture of the picture of the uncertain number. If you were to run an extremely large number of trials with extremely narrow bins, you histogram would approach the probability distribution, which displays all possible outcomes of the uncertain number.

The Cumulative Graph

The cumulative graph allows us to read the probability that the output cell is less than or equal to any particular number. This may be the most useful way to express an uncertainty to your boss.

The Mean, Mode and Median

The mean of an uncertain number can be thought of as the balance point of its histogram. Related concepts are the mode, the place with the tallest bar, and the median, the bar with equal weight to its right and left. In general the mean, mode and median will be different unless the histogram is symmetric.

The Variance and Standard Deviation

Several measures of the spread or degree of uncertainty of a number have been defined. A