Introduction: Why Descriptive Statistics Matter
Before you dive into inference and hypothesis testing, AP Statistics starts with descriptive statistics — the foundation of the course.
Descriptive statistics are all about:
- Summarizing data (center, spread, shape).
- Visualizing patterns (graphs and plots).
- Communicating clearly about distributions.
These concepts appear in Units 1 and 2 and are always tested on the AP exam, both in MCQs and FRQs.
RevisionDojo’s guide covers everything you need to know — from mean vs. median to z-scores and boxplots.
Step 1: Measuring the Center
Mean (average)
- Add values, divide by n.
- Affected by outliers.
Median
- Middle value when data is ordered.
- Resistant to outliers.
Mode
- Most frequently occurring value.
- Rarely important in AP Stats, but sometimes useful.
AP Exam Tip: Use mean for symmetric data, median for skewed data.
Step 2: Measuring Spread
Range
- Max – Min.
- Easy but unreliable (outliers distort).
Interquartile Range (IQR)
- 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.
