Download AP Statistics

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
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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
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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
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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
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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
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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
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Center
Median
Spread
Range
Quartile
Interquartile range (IQR)
Percentile
5-number summary
Box plot
Mean
More Vocabulary
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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
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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