Comparing distributions

**Comparison 1 (average):** Class X has a higher mean (65) than Class Y (58). This shows that on average, Class X performed better on the test. **Comparison 2 (spread):** Class X has a larger range (40) than Class Y (25). This shows that Class X's scores were more spread out, while Class Y performed more consistently. ✓

**Comparison of average:** Shop B has a higher median (52 sandwiches) than Shop A (45 sandwiches). This means Shop B typically sells more sandwiches per day. **Comparison of spread:** Shop A has a smaller IQR (12) than Shop B (28). This means the middle 50% of Shop A's sales are less spread out. **Which is more predictable:** **Shop A has more predictable sales** because: - The IQR is smaller, so daily sales vary less - Shop B's large IQR (28) means sales fluctuate more, making it harder to predict (Shop A would find it easier to plan stock levels) ✓

**Analysis of averages:** Athlete Q has a lower mean time (11.0s vs 11.2s), so on average, Q runs faster. **Analysis of spread:** Athlete P has a smaller standard deviation (0.15 vs 0.45), meaning P's times are more consistent and predictable. **Recommendation:** **It depends on the situation:** **Choose Athlete Q if:** You need the best possible time. Q's average is 0.2 seconds faster, which could make the difference. **Choose Athlete P if:** Consistency matters more. P is more reliable and unlikely to have a bad race. Q's high standard deviation means Q could run anywhere from ~10s to ~12s. **Most likely recommendation: Athlete P** for an important race, as consistency reduces risk. ✓