Decide whether the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The relative frequency of B grades in our class was 0.3 . Choose the correct answer below. A. The statement makes sense. Suppose there were 20 people in the class. If 4 received Bs and 2 received As, then the relative frequency of $$ B $$ grades was $$ \frac{4+2}{20}=\frac{6}{20}=0.3 $$. B. The statement makes sense. Suppose there were 20 people in the class. If 6 received Bs, then the relative frequency of B grades was $$ \frac{6}{20}=0.3 $$. C. The statement does not make sense. Statements about relative frequencies only make sense when the total number of data values is given. D. The statement does not make sense. Relative frequencies must be integers, and 0.3 is not an integer.

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UpStudy AI · Accepted Answer

To determine whether the statement "The relative frequency of B grades in our class was 0.3" makes sense, let's analyze the options provided:

1. **Understanding Relative Frequency**: 
   - Relative frequency is calculated as the number of occurrences of a specific event (in this case, B grades) divided by the total number of observations (total grades).
   - It can be expressed as a fraction, decimal, or percentage.

2. **Evaluating Each Option**:
   - **Option A**: "The statement makes sense. Suppose there were 20 people in the class. If 4 received Bs and 2 received As, then the relative frequency of B grades was $$ \frac{4+2}{20}=\frac{6}{20}=0.3 $$."
     - This option is incorrect because the calculation of relative frequency is wrong. The relative frequency of B grades should be $$ \frac{4}{20} = 0.2 $$, not 0.3. Therefore, this statement does not support the original claim.

- **Option B**: "The statement makes sense. Suppose there were 20 people in the class. If 6 received Bs, then the relative frequency of B grades was $$ \frac{6}{20}=0.3 $$."
     - This option is correct. If there are 20 students and 6 received B grades, then the relative frequency of B grades is indeed $$ \frac{6}{20} = 0.3 $$. This supports the original statement.

- **Option C**: "The statement does not make sense. Statements about relative frequencies only make sense when the total number of data values is given."
     - This option is misleading. While knowing the total number of data values helps in understanding the context, the statement itself can still be valid if we assume a total number of students. Therefore, this option does not accurately reflect the validity of the original statement.

- **Option D**: "The statement does not make sense. Relative frequencies must be integers, and 0.3 is not an integer."
     - This option is false. Relative frequencies are not required to be integers; they can be decimals or fractions. Thus, this statement is incorrect.

3. **Conclusion**:
   - The correct answer is **B**. The statement makes sense because it is possible to have a relative frequency of B grades equal to 0.3 if 6 out of 20 students received B grades.

Therefore, the final answer is **B**.
The statement makes sense. If 6 out of 20 students received B grades, the relative frequency is 0.3.

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