Data Collection and Statistics

Step 1: Find the original sum: $6 \times 15 = 90$

Step 2: Find the new sum: $7 \times 17 = 119$

Step 3: The 7th number = $119 - 90 = 29$

Check: $(90 + 29) \div 7 = 119 \div 7 = 17$ ✓

Answer: The 7th number is 29.

IQR: $Q_3 - Q_1 = 60 - 30 = 30$

Answer: YES — with appropriate caveats.

Why: This is a randomized controlled experiment, not just an observational study.

Key features that allow a causal conclusion:

1. Random assignment to treatment groups — this controls for confounding variables
2. Control group (traditional method) for comparison
3. Same number in each group

However, she should also consider:

• Statistical significance — is the 4-point difference large enough to not be due to chance? (She'd need a p-value or confidence interval.)
• Practical significance — is a 4-point difference meaningful in practice?

SAT Rule:

• Randomized experiment → CAN conclude causation
• Observational study → can only conclude ASSOCIATION

Set A has the larger standard deviation.

Reasoning: Both sets have the same mean:

• Set A: $\frac{10+12+14+16+18}{5} = 14$
• Set B: $\frac{12+13+14+15+16}{5} = 14$

Set A has values that are more spread out from 14 (ranging from 10 to 18, each value 2 units apart from the next).

Set B has values that are more tightly clustered around 14 (ranging from 12 to 16, each value only 1 unit apart).

Since standard deviation measures how far values are from the mean on average, Set A has the larger standard deviation.

Answer: Set A

SAT Tip: You don't need to calculate SD on the SAT — just understand that wider spread = larger SD.