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Comparing Two Distributions
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Comparing Two Distributions
📚 Part 1: Multiple Choice & Vocabulary
1. Which measure is most sensitive to extreme values (outliers)?
Mean
Median
Mode
Interquartile range (IQR)
2. In a box plot comparison, the IQR shows:
The middle 50% of the data
The complete spread from minimum to maximum
The mean of the distribution
The most frequent value
3. Check all statements that help when comparing two distributions:
Compare centers (mean or median)
Compare spread (range, IQR, MAD)
Compare shape (symmetric, skewed, peaks)
Compare overlap of the two distributions
Only compare the modes to decide which is larger
4. If two distributions have similar medians but one has a much larger IQR, you can conclude:
The distribution with larger IQR has more variability in the middle 50%
The distribution with larger IQR has a higher mean
The distributions have no overlap
The smaller IQR always means the data are skewed
✏️ Part 2: Calculations, Graphing, and Interpretation
Two classes' test scores (out of 110):
Class A: 78, 82, 85, 88, 90, 92, 95, 98
Class B: 70, 75, 80, 85, 90, 95, 100, 105
5. Calculate the mean and median for each class. Show your work.
6. Calculate the range and the IQR (show Q1 and Q3) for each class.
7. Sketch a pair of side-by-side box plots (double box plot) for Class A and Class B on the same number line. Label minimum, Q1, median, Q3, and maximum.
8. In 2–3 sentences, compare Class A and Class B in terms of shape, center, spread, and overlap. What informal inference can you draw about the two populations?
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