AP Statistics Descriptive Statistics Guide (2025 Study Guide)

• Q3 – Q1.
• Resistant to outliers.

Standard Deviation (s)

• Measures how spread out data is from the mean.
• Low s → data clustered. High s → data spread out.

Formula (sample SD):

s=∑(xi−xˉ)2n−1s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}

AP Exam Tip: Standard deviation always reported with the mean.

Step 3: Five-Number Summary

• Minimum
• Q1
• Median
• Q3
• Maximum

Used for boxplots.

Outlier Rule: A data point is an outlier if it is more than 1.5 × IQR above Q3 or below Q1.

Step 4: Visual Representations

Histogram

• Shows frequency distribution.
• Good for shape (skewed, symmetric).

Boxplot

• Based on five-number summary.
• Great for comparing two distributions.

Dotplot

• Simple but effective for small data sets.

Stemplot

• Useful for showing shape and detail.

RevisionDojo Tip: Always comment on shape, center, spread, outliers (SCOS).

Step 5: Z-Scores

A z-score measures how far a value is from the mean in standard deviations.

Formula:

z=x−xˉsz = \frac{x - \bar{x}}{s}

Example: A test score of 85 with mean = 75, SD = 5.

z=85−755=2z = \frac{85-75}{5} = 2

Interpretation: The score is 2 standard deviations above the mean.

Step 6: Describing Distributions

Always use SCOS:

• Shape: Symmetric, skewed left, skewed right.
• Center: Mean or median.
• Outliers: Any extreme values.
• Spread: IQR or standard deviation.

Example FRQ Answer:
“The distribution of AP Stats test scores is roughly symmetric with a mean of 72, standard deviation of 8, and no apparent outliers.”

Step 7: Normal Distribution

While technically part of probability, descriptive stats often include normal models.

• Empirical Rule (68-95-99.7 Rule).
• Standardized z-scores.
• Normal probability plots.

Step 8: Common Mistakes Students Make

• Forgetting to mention context (“mean = 72” vs. “mean score = 72 points”).
• Using mean with skewed data.
• Confusing range with IQR.
• Ignoring outliers in boxplots.
• Forgetting to connect z-scores to interpretation.

Step 9: How Descriptive Stats Appear on the AP Exam

• MCQs: Quick calculations (mean, z-score, IQR).
• FRQs: Writing full-sentence descriptions of distributions.
• Investigative Task: Comparing groups with boxplots.

Step 10: RevisionDojo Resources

RevisionDojo makes descriptive statistics easy with:

• Visual charts comparing mean/median/SD/IQR.
• Boxplot practice sets with answer explanations.
• SCOS templates for FRQ writing.
• Z-score drills with real-world examples.

These tools help you build automatic habits so you don’t forget exam-day details.

Frequently Asked Questions (FAQs)

Q: Which measure of center should I use?
A: Mean if symmetric, median if skewed.

Q: Do I always need to mention outliers?
A: Yes, even if “no apparent outliers.”

Q: How many decimals should I report?
A: Usually 2 decimals for AP Stats. Be consistent.

Q: Is range important?
A: Mention it if relevant, but IQR and SD are more reliable.

Q: Do I need to memorize the SD formula?
A: No, but you must understand what it means.

Final Thoughts

Descriptive statistics may seem basic, but they are fundamental for success in AP Stats.

• Always describe distributions with SCOS.
• Use mean + SD for symmetric data, median + IQR for skewed.
• Interpret z-scores and boxplots in context.

With RevisionDojo’s SCOS templates, boxplot drills, and visual guides, you’ll master descriptive statistics and set yourself up for success in later units — and ultimately a 5 on the AP Statistics Exam.