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AP Statistics Chapter 1 • Think – Where are you going, and why? • Show – Calculate and display. • Tell – What have you learned? Without this step, you’re never done. Interpret your results. READ THE BOOK!! Chapter 2 • Data is King! But only if it’s organized. – Context (who, what, when, where, how & why) – Data tables • Categorical vs. Quantitative Data – Sometimes a variable can take either role, depending on context. – Just because the variables are numbers doesn’t mean that they’re necessarily quantitative. – Always be skeptical. • Counts count Vocabulary • • • • • • • • Context Data Data Table Case Variable Quantitative Variable Qualitative Variable Units Skills • Be able to: – recognize the six questions. – ID the cases and variables in any data set. – Classify a variable as quantitative or qualitative depending on its use. – ID units for quantitative data in which the variable has been measured (or not the omission). Chapter 3 Displaying and Describing Categorical Data • The three rules of data analysis: – Make a picture – Make a picture – Make a picture • Displaying data: – The area principle – Bar charts – Pie charts Contingency Tables The Titanic • A contingency table is a 2-way table that shows how individuals are distributed along each variable, contingent on the value of the other value. • When summed along rows and columns, frequency distributions can be shown (marginal distribution). • Conditional distribution – shows distribution of one variable for just the individuals who satisfy some condition on another variable. Vocabulary • • • • • • • • • • • Frequency table Relative frequency table Distribution Area principle Bar chart Pie chart Contingency table Marginal distribution Conditional distribution Independence Simpson’s paradox Chapter 4 Displaying Quantitative Data • Some types of displays – Histograms – Stem-and-Leaf plots – Dot plots • Shape, Center and Spread – Unimodal, bimodal or multimodal – Symmetry & skewness – Outliers Analyzing Distributions • • • • Comparing distributions Time plots Re-expressing skewed data to improve symmetry What could possibly go wrong? – Don’t make histograms of categorical data – Don’t look for shape, center & spread if the data’s categorical – Don’t confuse bar charts and histograms – Use appropriate scales, bin widths and labels Vocabulary • • • • • • • • • • Distribution Histogram (relative frequency histogram) Stem-and-leaf display Dotplot Shape (single vs. multiple modes, symmetry vs. skewness) Center Spread Mode Unimodal Uniform More Vocabulary • • • • • Symmetric Tails Skewed Outliers Timeplot Chapter 5 Describing Distributions Numerically • Center of the Distribution – Mean or Median? • The spread – Range = max – min – The interquartile range (IQR) – 25th percentile to the 75th percentile – The 5-number summary Box Plots • Box Plots – Graphically displays the 5-number summary – Can show outliers – Useful to compare to histogram • Comparing groups with box blots – 5-number summary – Common scale Summarizing Symmetric Distributions • Mean or average • Mean or median? • Spread – variance – standard deviation • . . . Which comes down to shape, center and spread Vocabulary • • • • • • • • • • Center Median Spread Range Quartile Interquartile range (IQR) Percentile 5-number summary Box plot Mean More Vocabulary • • • • Variance Standard deviation Comparing distributions Comparing box plots Chapter 6 The Standard Deviation and the Normal Model • Standard deviation as a ruler • Standardizing with z-scores – data based: – Standardized values (Z) – Shifting data – Rescaling data • The Normal Model & the Bell-Shaped Curve – Model based (parameters): – Nearly Normal condition (unimodal and symmetric) More about the Normal Model • The mean is shifted to zero, and the standard deviation is one • Adding versus rescaling • The 68-95-99.7 rule – 68% of values fall within 0 ± 1𝜎 – 95% of values fall within 0 ± 2𝜎 – 99.7% of values fall within 0 ± 3𝜎 • Using the z-table, and finding values using technology • From percentiles to scores: z in reverse • Normal probability plot Vocabulary • • • • • • • • • • • Standardizing Standardized value Normal model Parameter Statistic Z-score Standard normal model 68-95-99.7 rule Normal percentile Normal probability plot Changing center and spread