In a class of 40 students, the following data were collected on their favorite sport: Soccer 10 students, Basketball: 15 students, Tennis: 5 students, Swimming: 10 students. What is the relative frequency of students whose favorite sport is not basketball?

Rationale

The relative frequency of students whose favorite sport is not basketball is 0.625.

To find this relative frequency, we first determine the number of students who do not favor basketball. There are 40 students in total, and 15 prefer basketball, which means 25 students prefer other sports. The relative frequency is then calculated as the number of students not favoring basketball (25) divided by the total number of students (40), resulting in 0.625.

A (0.25) YOUR ANSWER

This value represents a ratio that would imply only 10 students favor sports other than basketball, which is incorrect. The calculation for 0.25 would be 10 divided by 40, leading to an inaccurate conclusion about students' preferences.

B (0.5) YOUR ANSWER

A relative frequency of 0.5 would suggest that 20 students prefer sports other than basketball. This is not consistent with the data collected, as only 25 students favor other sports. Therefore, this option misrepresents the actual distribution.

C (0.625) CORRECT

This choice accurately reflects the proportion of students whose favorite sport is not basketball. With 25 out of 40 students favoring other sports, dividing 25 by 40 gives a relative frequency of 0.625, correctly representing the majority preference.

D (0.75) YOUR ANSWER

Selecting 0.75 would imply that 30 students prefer sports other than basketball. However, the data shows that only 25 students fall into this category, making this option incorrect in light of the total student count.

Conclusion

In summary, the calculation of relative frequency reveals that 0.625 is the accurate representation of students whose favorite sport is not basketball. By analyzing the data of 40 students, we find that 25 students prefer other sports, confirming this relative frequency as the correct answer. All other options either miscalculate or misinterpret the given data.

In a class of 40 students, the following data were collected on their favorite sport: Soccer 10 students, Basketball: 15 students, Tennis: 5 students, Swimming: 10 students. What is the relative frequency of students whose favorite sport is not basketball?

The relative frequency of students whose favorite sport is not basketball is 0.625.

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