Unit 1 covers how to display and describe distributions of one-variable data using graphical and numerical summaries — the foundational skills for all statistical analysis.
Categorical: bar chart, pie chart. Quantitative: dotplot, histogram, stemplot, boxplot. Describe distributions using SOCS: Shape (symmetric, skewed left/right, unimodal/bimodal), Outliers (unusual observations), Centre (mean, median), Spread (range, IQR, standard deviation). Mean: sensitive to outliers (pulled toward extreme values). Median: resistant to outliers. Use median for skewed distributions.
Range: max − min. IQR: Q3 − Q1 (middle 50%). Outlier rule: below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Standard deviation: average distance from mean. z-score: z = (x − μ)/σ (how many SDs from mean). Normal distribution: symmetric, bell-shaped. Empirical rule: 68-95-99.7% within 1-2-3 SDs. Use z-table or calculator for normal probabilities.
Use the mean when the distribution is roughly symmetric and has no strong outliers — it uses all data values. Use the median when the distribution is skewed or has outliers — it is resistant (not affected by extreme values). For example: household income is right-skewed (a few very high incomes), so median income ($70,000) is more representative than mean income ($100,000+). Report mean with standard deviation, median with IQR. On the AP exam, always explain your choice of measure in context of the distribution\'s shape.
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