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# Summarizing quantitative data

AP Stats: UNC (BI), UNC‑1 (EU), UNC‑3 (EU)

AP Stats: UNC (BI), UNC‑1 (EU), UNC‑1.I (LO), UNC‑1.I.1 (EK), UNC‑1.I.2 (EK), UNC‑1.I.3 (EK)

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Statistics intro: Mean, median, & modeMean, median, & mode exampleMedian in a histogram

Practice

Calculating the meanGet 3 of 4 questions to level up!

Calculating the medianGet 3 of 4 questions to level up!

Calculating mean and median from data displaysGet 3 of 4 questions to level up!

AP Stats: UNC (BI), UNC‑1 (EU), UNC‑1.I (LO), UNC‑1.I.2 (EK), UNC‑1.K (LO), UNC‑1.K.2 (EK), UNC‑1.M (LO), UNC‑1.M.2 (EK)

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Mean as the balancing pointMissing value given the meanImpact on median & mean: increasing an outlierImpact on median & mean: removing an outlierEstimating mean and median in data displays

Practice

Missing value given the meanGet 3 of 4 questions to level up!

Effects of shifting, adding, & removing a data pointGet 3 of 4 questions to level up!

Estimating mean and median in data displaysGet 3 of 4 questions to level up!

AP Stats: UNC (BI), UNC‑1 (EU), UNC‑1.J (LO), UNC‑1.J.1 (EK), UNC‑1.J.2 (EK), UNC‑1.J.3 (EK), UNC‑1.K (LO), UNC‑1.K.2 (EK)

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Interquartile range (IQR)Sample varianceSample standard deviation and biasVisually assessing standard deviationMean and standard deviation versus median and IQR

Practice

Interquartile range (IQR)Get 3 of 4 questions to level up!

Sample standard deviationGet 3 of 4 questions to level up!

Visually assessing standard deviationGet 3 of 4 questions to level up!

AP Stats: UNC (BI), UNC‑1 (EU), UNC‑1.J (LO), UNC‑1.J.3 (EK), UNC‑3 (EU), UNC‑3.I (LO), UNC‑3.I.1 (EK)

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Review and intuition why we divide by n-1 for the unbiased sample varianceWhy we divide by n - 1 in variance Simulation showing bias in sample varianceSimulation providing evidence that (n-1) gives us unbiased estimateUnbiased estimate of population variance

AP Stats: UNC (BI), UNC‑1 (EU), UNC‑1.K (LO), UNC‑1.K.1 (EK), UNC‑1.L (LO), UNC‑1.L.1 (EK), UNC‑1.L.2 (EK)

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Worked example: Creating a box plot (odd number of data points)Worked example: Creating a box plot (even number of data points)Reading box plotsInterpreting box plotsJudging outliers in a dataset

Practice

Creating box plotsGet 3 of 4 questions to level up!

Reading box plotsGet 3 of 4 questions to level up!

Interpreting quartilesGet 3 of 4 questions to level up!

Identifying outliersGet 3 of 4 questions to level up!

### About this unit

This unit covers common measures of center like mean and median. We'll also learn to measure spread or variability with standard deviation and interquartile range, and use these ideas to determine what data can be considered an outlier.AP® is a registered trademark of the College Board, which has not reviewed this resource.