The Survey Results Paragraph
A student writes a paragraph for a class report: "The survey asked 50 students about sport. Most students said they played sport. 32 students played soccer and 21 played netball. Some students played both. Only 4 students played no sport at all. This shows that sport is very popular and the school should build a new soccer field."
A classmate points out that the numbers do not simply add up, and that the conclusion may not follow from the data.
1. Explain why 32 + 21 cannot simply be added to find how many students play sport.
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The paragraph says "some students played both." If a student plays both soccer and netball, they are counted once in the 32 and again in the 21. Adding gives 53, which is more than the 50 students surveyed - impossible.
So the number who play at least one sport is 53 minus the number who play both. We are not told that overlap number, so we cannot calculate it exactly.
Answer: The two groups overlap, so adding double-counts students who play both. The total playing sport is fewer than 53.
2. Does the data support building a new soccer field? Give a reasoned judgement.
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The data shows sport is popular, but it does not show soccer is more popular than netball in a way that justifies a soccer field. 32 played soccer, 21 netball, but we do not know how many play both. If many play both, the gap between the sports is small.
Also, "most students played sport" is vague, and 4 played none. The survey does not ask whether students want a new field or what facilities they need.
Answer: The conclusion goes beyond the evidence. The data supports "sport is popular" but not specifically a new soccer field. More information, such as student preferences, is needed.