When the target of inference is a group mean rather than an individual score, long assessments can be statistically inefficient. From the marginal score of the likelihood, we derive the asymptotic standard error of the marginal maximum likelihood estimator of a latent IRT mean under random item sampling, and obtain a closed-form approximation via a Gaussian-convolution treatment of the item information. The formula makes the test-length--sample-size trade-off explicit and includes an inflation factor for jointly estimating the population variance when the item pool is mistargeted. We validate it against exact benchmarks, Monte Carlo simulation under pool--population mismatch, and a NAEP mathematics resampling study; group means remain approximately unbiased even with single-item forms.

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