To analyze the claims made by Tara and Jim, we need to consider the survey data and the ratios they provided.
Survey Results
- Morning exercises: 35 people
- Afternoon exercises: 45 people
- Night exercises: 20 people
- Total people surveyed: 100
Jim's Claim
Jim claims the ratios of:
- Morning: \( \frac{35}{100} \)
- Afternoon: \( \frac{45}{100} \)
- Night: \( \frac{20}{100} \)
These are valid because the total number of people in the survey is 100, so representing the number of people exercising at different times as a fraction of the total makes sense. Thus, Jim's claim is correct.
Tara's Claim
Tara claims the ratios of:
- Morning: \( \frac{35}{55} \)
- Afternoon: \( \frac{45}{80} \)
- Night: \( \frac{20}{65} \)
Let's examine these claims individually:
-
Morning ratio: \( \frac{35}{55} \)
- This ratio suggests that Tara is claiming there’s a group of 55 people in total who exercise in the morning. However, there are 100 people surveyed in total. Thus, this ratio does not appropriately reflect the total surveyed, and therefore it's not valid as a ratio of the survey's total.
-
Afternoon ratio: \( \frac{45}{80} \)
- Again, Tara is stating that there are 80 people in total, which does not match the 100 people surveyed. This makes the ratio invalid.
-
Night ratio: \( \frac{20}{65} \)
- Similar reasoning applies. Claiming a total of 65 people does not match the total surveyed of 100, making this ratio invalid as well.
Conclusion
- Jim's claim is valid as the ratios reflect the correct total of people in the survey.
- Tara's claim is not valid because she uses incorrect denominators that do not correspond to the total number of people surveyed.
Overall, Jim's ratios provide a legitimate representation of the data collected from the survey.
2 answers