AP Statistics Exam Review - Flashcards

1-Variable Distribution Description

• Use SOCS (Shape, Outliers, Center, Spread) along with context for a complete description.

Distribution Shape

• Symmetric: Balanced on both sides of the center.
• Skewed Right: Tail extends to the right; fewer values in the right tail.
• Skewed Left: Tail extends to the left; fewer values in the left tail.
• Incorporate -ly adverbs (e.g., fairly, slightly) when describing shape.

Outlier Formulas

• High outlier: ( Q3 + 1.5 \times \text{IQR} )
• Low outlier: ( Q1 - 1.5 \times \text{IQR} )

Measures of Center

• Mean and median are common; mode is not used in this context.

Measures of Spread

• Spread can be measured using range, standard deviation, and IQR.
• Standard deviation and IQR offer more precision than range.

Center and Spread for Symmetric Distribution

• Center is determined by the mean.
• Spread is measured using standard deviation.

Center and Spread for Skewed Distribution

• Center is found using the median.
• Spread is best represented by the IQR.

IQR Calculation

• Interquartile Range (IQR) is calculated as ( Q3 - Q1 ).

Standard Deviation

• Represents the average distance of values from the mean, indicating spread or variability.

Sample Distribution Description

• For example, sleep hours: "The distribution of hours of sleep is slightly skewed left, with a median of 7 and an IQR of 1. There is one outlier at 3."

Tips for 1-Variable Distributions

• Use calculator functions like 1-VARSTATS for accurate results.
• Always establish context in descriptions.

Displays for 1-Variable Data

• Data can be visualized using histograms, dotplots, boxplots, and stemplots.

Finding Median from Histogram

• Sum frequencies to find total; find the middle value accordingly.

Standard Deviation from Dotplot

• Wider data indicates smaller standard deviation; narrower data results in larger standard deviation.

Example of 5-Number Summary

• Minimum: 2, Q1: 18, Median: 23, Q3: 33, Maximum: 58; IQR is 15.
• Use a single value for IQR; outliers are indicated distinctly in box plots.

Stemplot Shape Comparison

• More data at lower ends indicates right skew; more data at higher ends indicates left skew.
• Include a key and title for clarity in displays.

2-Variable Data Description

• Use DUFS (Direction, Unusual features, Form, Strength) with context when analyzing scatterplots.

Direction of 2-Variable Data

• It can be either positive or negative.

Unusual Features in 2-Variable Data

• Identify any outliers or clusters present in the data.

Form of 2-Variable Data

• Determine if the relationship is linear or nonlinear.

Strength of 2-Variable Data

• Descriptive strength categories include weak, moderate, or strong.

Example Description of 2-Variable Data

• "There is a strong negative linear relationship between average temperature and heating bills with no outliers."

Interpretation of Slope in Linear Regression

• Expresses the change in the response variable for every one-unit change in the explanatory variable.