The basketball players at Rafael’s middle school are selling T-shirts, and he wants to determine the average number of shirts that have been sold. First he surveyed five members of the 7th-grade boys basketball team. Then he surveyed every third basketball player on the boys and girls 6th- through 8th-grade basketball teams. Which sampling technique should produce a more representative sample?
Answer
A
The first sampling method (7th graders) is the most representative.
B
The second sampling method (6th–8th graders) is the most representative.
C
Both samples should be exactly the same.
D
Neither sample will be representative.
Explanation
The second method surveys players from both boys’ and girls’ teams across grades 6 through 8, so it includes more of the groups whose shirt sales Rafael wants to estimate. The first method surveys only five 7th-grade boys, which leaves out other grades and girls and may not reflect the whole group. Therefore, surveying every third player across all the teams should produce a more representative sample.
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