In a reaction-time experiment, Study A consists of 72 trials with a total recorded reaction time of 32.4 seconds.Study B...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
- In a reaction-time experiment, Study A consists of \(\mathrm{72}\) trials with a total recorded reaction time of \(\mathrm{32.4}\) seconds.
- Study B consists of \(\mathrm{48}\) trials with a mean reaction time of \(\mathrm{0.65}\) second per trial.
- When the results of Studies A and B are combined into a single data set, what is the mean reaction time, in seconds per trial, of the combined data set? Express your answer as a decimal to the nearest hundredth.
1. TRANSLATE the problem information
- Study A: 72 trials with total recorded time of 32.4 seconds
- Study B: 48 trials with mean time of 0.65 seconds per trial
- Goal: Find the mean reaction time when both studies are combined
2. INFER the approach needed
- Study A gives us total time directly, but Study B gives us mean time per trial
- To combine data sets properly, we need both total times and both trial counts
- Strategy: Convert Study B's information to total time, then combine everything
3. SIMPLIFY to find Study B's total time
- Total time = number of trials × mean per trial
- Study B total time = \(48 \times 0.65 = 31.2\) seconds (use calculator)
4. SIMPLIFY to combine the data sets
- Combined total time = \(32.4 + 31.2 = 63.6\) seconds
- Combined total trials = \(72 + 48 = 120\) trials
5. SIMPLIFY to find the combined mean
- Combined mean = total time ÷ total trials
- Combined mean = \(63.6 \div 120 = 0.53\) seconds per trial (use calculator)
Answer: 0.53
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students try to average the two means instead of properly combining data sets.
They calculate: Mean of Study A = \(32.4 \div 72 = 0.45\), then try to find \((0.45 + 0.65) \div 2 = 0.55\). This incorrectly treats both studies as equally weighted when Study A actually has more trials. This leads to an incorrect answer of approximately 0.55.
Second Most Common Error:
Poor TRANSLATE reasoning: Students misunderstand what "total recorded reaction time" means for Study A.
They might think 32.4 seconds is the mean for Study A rather than the total time, leading them to calculate: Combined mean = \((32.4 + 0.65) \div 2 = 16.525\). This leads to confusion and abandoning systematic solution.
The Bottom Line:
This problem tests whether students understand that combining data sets requires working with totals, not just averaging existing means. The key insight is recognizing that different sample sizes must be properly weighted in the final calculation.