Unit 8 Summary

Pre-Algebra · Axiom Academy

SUMMARY Data Analysis and Statistics How we organize, summarize, and interpret data — turning a pile of numbers into a story we can actually read. Organize first: ordering values and building a frequency table reveals patterns and makes every other statistic easier to find. Always report center and spread. The mean follows every value (so it chases outliers); the median sits at the middle and resists them. Spread has three rulers: the range ( ), the standard deviation (typical distance from the mean), and the resistant IQR ( Q_3 - Q_1 ). The five-number summary — median — drives the box plot and the rule for flagging outliers. Match the display to the question, and read data critically: watch the axis scale, question the source, and remember correlation is not causation. Core Concept Data Types & Organization Before you compute anything, name what kind of data you have and put it in order. Categorical: describes a quality (favorite color, type of pet, city). Numerical: measured or counted numbers — discrete (counts with gaps, like siblings) or continuous (a scale, like height or time). Frequency table: counts how often each value or interval appears. Watch out for: the right summary depends on the type — you can't average a category. Core Concept Measures of Center Three ways to name the "typical" value — each answers the question differently. Mean: the average; sensitive to outliers and extreme values. Median: the middle value when ordered; resistant to outliers.

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