Data Distributions and Regression

Explore center and spread, regression and residual, outliers and association.

Lesson 4 of 53 parts Practice Flashcards

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Center and Spread

Objective: Explain center and spread and use it to solve or interpret a problem.

Mean and median summarize center differently; outliers can pull a mean more than a median. Spread must be considered before comparing groups. No, groups may have very different spreads.

Worked examples

Try itData Distributions and Regression — practice 1.1: Find the mean of 1, 5, and 9.Show answer

Step 1: Add the values: 1+5+9=15. Step 2: Divide by three observations. Step 3: The mean is 5.

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Center and Spread

Objective: Explain center and spread and use it to solve or interpret a problem.

Mean and median summarize center differently; outliers can pull a mean more than a median. Spread must be considered before comparing groups. No, groups may have very different spreads.

Worked examples

Try itData Distributions and Regression — practice 1.1: Find the mean of 1, 5, and 9.Show answer

Step 1: Add the values: 1+5+9=15. Step 2: Divide by three observations. Step 3: The mean is 5.

Regression and Residual

Objective: Explain regression and residual and use it to solve or interpret a problem.

A fitted line predicts outputs; residual=observed−predicted. Plotting residuals can reveal curvature or uneven spread that a single score hides. The observed output is above the prediction.

Worked examples

Try itData Distributions and Regression — practice 2.1: Observed y is 22 and predicted y is 20. Find the residual.Show answer

Step 1: Residual = observed − predicted. Step 2: Subtract 22−20. Step 3: The residual is 2.

Outliers and Association

Objective: Explain outliers and association and use it to solve or interpret a problem.

A possible outlier deserves investigation, not automatic deletion. Association alone does not prove a causal effect because other factors may matter. No, verify measurement and context before any exclusion.

Worked examples

Try itData Distributions and Regression — practice 3.1: Find median of 14, 8, and 11.Show answer

Step 1: Order the values 8, 11, 14. Step 2: Select the middle of three values. Step 3: The median is 11.

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