A group of 120 seventh- and eighth-grade students were asked whether they participate in sports or in non-sports-related activities. The two-way table shows their answers.
Participation in Sports or Non-Sports
| | Sports | Non-Sports | Total |
| :----- | :----- | :--------- | :---- |
| Seventh Grade | 39 | 24 | 63 |
| Eighth Grade | 29 | 28 | 57 |
| Total | 68 | 52 | 120 |
Which statement is correct?
A. Twenty-nine seventh-grade students chose a sports activity.
B. Twenty-eight eighth-grade students chose a sports activity.
C. Twenty-four seventh-grade students chose a nonsports activity.
D. Thirty-nine eighth-grade students chose a nonsports activity.
Answer (2)
Analyze the two-way table to verify each statement.
Check the number of seventh-grade students in sports: 39, not 29.
Check the number of eighth-grade students in sports: 29, not 28.
Check the number of seventh-grade students in non-sports: 24. This statement is correct.
Check the number of eighth-grade students in non-sports: 28, not 39.
The correct statement is: Twenty-four seventh-grade students chose a nonsports activity.
Explanation
Analyze the problem and data We are given a two-way table that shows the participation of seventh- and eighth-grade students in sports and non-sports activities. Our task is to identify the correct statement based on the data in the table.
Verify each statement against the table Let's examine each statement:
Twenty-nine seventh-grade students chose a sports activity.
According to the table, 39 seventh-grade students participate in sports, not 29. So, this statement is incorrect.
Twenty-eight eighth-grade students chose a sports activity.
The table shows that 29 eighth-grade students participate in sports, not 28. Thus, this statement is also incorrect.
Twenty-four seventh-grade students chose a nonsports activity.
The table indicates that 24 seventh-grade students participate in non-sports activities. This statement is correct.
Thirty-nine eighth-grade students chose a nonsports activity.
The table shows that 28 eighth-grade students participate in non-sports activities, not 39. Therefore, this statement is incorrect.
Identify the correct statement Based on our analysis, the only correct statement is:
Twenty-four seventh-grade students chose a nonsports activity.
Examples
Two-way tables are commonly used to analyze survey data in various fields, such as market research or social sciences. For example, a company might use a two-way table to analyze customer preferences for different product features based on demographic groups, helping them tailor their marketing strategies.
After analyzing the two-way table, the only correct statement is that twenty-four seventh-grade students chose a nonsports activity. The other statements were found to be incorrect based on the data provided.
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