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 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) – 25 th percentile to the 75 th percentile – The 5-number summary

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 rule – 68% of values fall within 0 ± 1 – 95% of values fall within 0 ± 2 – 99.7% of values fall within 0 ± 3 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 rule Normal percentile Normal probability plot Changing center and spread