Data Analysis Summary

Algebra 1 · Axiom Academy

SUMMARY Data Analysis and Sequences A recap of how we describe datasets and recognize the patterns inside arithmetic and geometric sequences. Pick a display for the question you're asking: histograms reveal the shape of a distribution, box plots expose the five-number summary and outliers, scatter plots reveal relationships between two variables. The mean follows every value (and so chases outliers); the median sits at the middle and resists them. Match the measure of center to the data. Spread has three rulers: range ( ), standard deviation (typical distance from the mean), and the IQR ( Q_3 - Q_1 , the resistant one). An arithmetic sequence adds a constant difference d ; a geometric sequence multiplies by a constant ratio r . Classify by testing differences first, then ratios. Each pattern has a direct (explicit) term formula and a closed-form series sum, so you never have to list every term to reach the n th one. Core Concept Statistical Displays Different displays surface different features, so choose the one that answers your question. Histogram: frequency distribution — reveals shape (symmetric, skewed, uniform). Box plot: the five-number summary ( , Q_1 , median, Q_3 , ); flags outliers. Scatter plot: the relationship between two variables (positive, negative, or no correlation). Watch out for: correlation in a scatter plot does not prove causation — and always read the axis labels. Two questions about any dataset: where is its center, and how spread out is it?

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