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AP Statistics Unit One Overview

Sep 1, 2025

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Overview

This lecture covers the fundamentals of AP Statistics Unit One, including types of data, data representation, key statistical terms, describing distributions, and the basics of normal distributions.

Types of Data

  • Quantitative data consists of numerical values (e.g., height, population size).
  • Categorical data consists of named categories or labels (e.g., eye color, hair color).

Two-Way Tables & Relative Frequencies

  • Two-way tables display categorical data for two variables.
  • Marginal relative frequency is the proportion for a single row or column out of the total.
  • Joint relative frequency is the proportion at a particular cell (intersection of two variables) out of the total.
  • Conditional relative frequency is the proportion within a specific group (row/column) given a condition.

Describing Quantitative Data (SOCS)

  • Context: Always describe data in relation to what is measured.
  • Shape: Identify if the distribution is symmetrical, skewed, or unimodal.
  • Outliers: Note any extreme values away from the bulk of data.
  • Center: Use mean (average) or median (middle value).
  • Spread: Use range, standard deviation, or interquartile range (IQR).
  • Use comparative and descriptive language when describing data.

Key Statistical Terms

  • Mean: Sum of values divided by the number of values (average).
  • Standard deviation: Measures typical variation from the mean.
  • Median: Middle value in an ordered data set (50th percentile).
  • Range: Difference between maximum and minimum values.
  • Five-number summary: Min, Q1 (25th percentile), Median, Q3 (75th percentile), Max.
  • IQR: Interquartile range, calculated as Q3 minus Q1.

Outliers & Boxplots

  • Low-end outlier: Value less than Q1 − 1.5 × IQR.
  • High-end outlier: Value greater than Q3 + 1.5 × IQR.
  • Boxplots visually display the five-number summary.

Percentiles & Frequency

  • Percentile: Percent of values less than or equal to a specific value.
  • Cumulative relative frequency: Running total of percentage up to each value or interval.
  • Relative frequency: Proportion of occurrences over the total.

Z-Scores & Transformations

  • Z-score: Number of standard deviations a value is from the mean; formula: (value − mean) / standard deviation.
  • Adding/subtracting to all values shifts the center but does not change shape or spread.
  • Multiplying/dividing all values affects both center and spread, but not the shape.

Density Curves & Normal Distribution

  • Density curve: Continuous graph with area 1, representing probability distribution.
  • Normal distribution: Bell-shaped density curve; governed by mean and standard deviation.
  • 68-95-99.7 rule: 68% within 1 SD, 95% within 2 SDs, 99.7% within 3 SDs of mean.
  • Calculator functions: Normal PDF (probability at value), Normal CDF (probability in interval), Inverse Normal (find value from percentile).

Normal Probability Plots

  • Normal probability plot compares actual data values vs. expected Z-values for normality.
  • Roughly linear plot suggests data are approximately normal; non-linear indicates non-normality.

Key Terms & Definitions

  • Quantitative data — Numeric data representing quantity.
  • Categorical data — Data sorted into categories or labels.
  • Marginal relative frequency — Proportion in one row/column vs. total.
  • Joint relative frequency — Proportion at a cell vs. total.
  • Conditional relative frequency — Proportion within a specified group.
  • Mean — Arithmetic average of data.
  • Median — Middle value when data are ordered.
  • Standard deviation — Typical deviation from the mean.
  • IQR (Interquartile Range) — Difference between Q3 and Q1.
  • Z-score — Standardized value indicating SDs from mean.
  • Density curve — Graph representing probability distribution.
  • Normal distribution — Symmetrical, bell-shaped density curve.
  • Normal probability plot — Graph comparing data to a normal distribution.

Action Items / Next Steps

  • Practice identifying data types and constructing two-way tables.
  • Review calculator commands for normal distribution problems.
  • Practice drawing and interpreting boxplots.
  • Complete assigned homework/readings on normal distributions and data summaries.

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