AP Statistics Exam Review

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Questions and Answers

How do you describe a 1-variable distribution?

SOCS + context

Which of the following describes the shape of a distribution?

Symmetric

Skewed right

Skewed left

All of the above (correct)

What is the outlier formula for a value that is too high?

Q3 + 1.5 (IQR)

What is the outlier formula for a value that is too low?

< Q1 - 1.5 (IQR) Signup and view all the answers

Which of the following are ways to measure the center of a distribution?

Mean Signup and view all the answers

What are ways to measure the spread of a distribution?

All of the above Signup and view all the answers

How do you determine the center and spread of a symmetric distribution?

Center = mean, Spread = standard deviation Signup and view all the answers

How do you determine the center and spread of a skewed distribution?

Center = median, Spread = IQR Signup and view all the answers

What is the IQR formula?

Q3 - Q1 Signup and view all the answers

What is standard deviation?

A measure of spread/variability that gets the average distance from the mean Signup and view all the answers

What is the description for a 1-variable distribution of hours of sleep given the dataset: 3, 5, 6, 6, 7, 7, 7, 7, 8, 8?

The distribution is slightly skewed left, median is 7, IQR is 1, with one outlier. Signup and view all the answers

What is a tip for handling 1-variable distributions?

Put numbers into a list in your calculator and use 1-VARSTATS to check your answers. Signup and view all the answers

What are types of displays for 1-variable data?

All of the above Signup and view all the answers

How can you obtain the median of a histogram?

Add up the frequency of each number and find the middle value. Signup and view all the answers

How does data distribution affect standard deviation based on a dotplot?

Wider data results in smaller standard deviation, narrower data leads to larger standard deviation. Signup and view all the answers

What is an example of a 5-number summary from a box plot?

Minimum: 2, First-quartile: 18, Median: 23, Third-quartile: 33, Maximum: 58, IQR = 15. Signup and view all the answers

How do you interpret the shape in a stemplot?

If more data is at the lower ends, it's skewed right; if more data is at the higher ends, it's skewed left. Signup and view all the answers

What does a stemplot key like '1|0' mean?

10 Signup and view all the answers

How do you describe the distribution of 2-variable data?

DUFS + context Signup and view all the answers

What describes the direction of 2-variable data?

Positive or negative Signup and view all the answers

How do you describe unusual features in 2-variable data?

Look out for outliers or clusters. Signup and view all the answers

What terms can describe the form of 2-variable data?

Linear or nonlinear Signup and view all the answers

How would you describe the strength of 2-variable data?

Weak, moderate, or strong Signup and view all the answers

Can you provide an example of a description of 2-variable data?

There is a strong, negative, linear relationship between average temperature and heating bills, with no outliers. Signup and view all the answers

How do you interpret the slope of a linear regression line?

For every 1 unit increase in the explanatory variable x, the dependent variable changes by the slope amount. Signup and view all the answers

Study Notes

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.

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Prepare for your AP Statistics exam with this comprehensive flashcard set. Explore important concepts like how to describe a 1-variable distribution and the shape of distributions, ensuring you're ready for the exam. Use this study tool to reinforce your understanding of key statistical terms.

AP Statistics Exam Review - Flashcards

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