Probability and Statistics Summary

Algebra 2 · Axiom Academy

SUMMARY Probability and Statistics Summary Let's review how we quantify uncertainty and extract meaning from data to make informed decisions. Center and spread together describe a data set: mean, median, and mode locate its "typical" value, while range, variance, and describe how spread out it is. A box plot's five-number summary (min, Q_1 , median, Q_3 , max) reveals shape and outliers at a glance — the IQR measures the spread of the middle 50%. A random variable's expected value is its long-run average; the binomial distribution models a fixed number of independent yes/no trials. For a normal distribution, the empirical rule says about 68%, 95%, and 99.7% of values fall within 1, 2, and 3 standard deviations of the mean. The probability rules — complement, addition, multiplication, and conditional — combine with counting (the Fundamental Counting Principle, permutations, combinations) to compute the likelihood of anything, however complex. Core Concept Measures of Center Mean, median, and mode all describe a data set's "typical" value, but they tell different stories. The mean is the arithmetic average; the median is the middle value when data is ordered; the mode is the most frequent value. When to use: mean for roughly symmetric data; median when data is skewed or has outliers. Watch out for: a single extreme outlier can drag the mean far from where most of the data actually sits. Core Concept Measures of Spread

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