Two groups and one denominator
In a fictional training exercise, Group A contains 20 participants with a mean score of 60 on a classroom practice activity. Group B contains 30 participants with a mean score of 80 on the same activity and scale. The teacher has not supplied individual scores, variances, medians or a sampling design. A student averages 60 and 80 and calls 70 the combined mean. Another claims the larger mean proves Group B received better instruction, although participants were not randomly assigned and prior preparation is unknown. The class must distinguish a calculation determined by the supplied totals from an interpretation the record cannot establish. These scores are invented for the exercise, have no relationship to an official examination scale, and do not describe actual learners or a measured intervention.
1. Calculate the combined mean with its denominator.
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The group totals are 20 times 60=1200 and 30 times 80=2400. Their combined sum is 3600 across 50 participants, giving a mean of 72. Averaging the two group means without weights would incorrectly give equal influence to unequal counts.
2. What causal conclusion or distribution comparison remains unsupported?
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The record does not establish that instruction caused the mean difference, because prior preparation and selection are unknown. It also does not supply the medians or spread, so those features cannot be recovered from the means and counts alone.