What happens to variability in summary statistics when the number of trials in a simulation increases?

• A. It increases.
• B. It remains the same.
• C. It decreases.
• D. It becomes unpredictable.

Answer: (C)

Increasing the number of trials makes the estimate more precise because random fluctuations cancel out more as you sample more. As you gather more independent observations, the sampling distribution of the summary statistic tightens around the true value. For the mean, the typical measure of this spread is the standard error, which scales as sigma divided by the square root of the number of trials; doubling the trials reduces the standard error by about 29% (since it’s divided by sqrt(2)). In general, the variability of the estimated summary statistics decreases with more trials, making results more stable across repeated runs. This reflects the idea that more data reduces sampling error, though it doesn’t eliminate the intrinsic randomness of each trial.