Questions: Rafael is taking a self-paced math class. His scores for each of the 15 quizzes during the academic year are shown below. Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6.) Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage. Quiz score: 89, 85, 72, 66, 76, 68, 80, 83, 71, 68, 81, 67, 70, 78, 67. Quiz score - Relative frequency: 66 to 71 - , 72 to 77 - , 78 to 83 - , 84 to 89 - .

Rafael is taking a self-paced math class. His scores for each of the 15 quizzes during the academic year are shown below.
Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6.)
Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.

Quiz score:
89, 85, 72, 66, 76,
68, 80, 83, 71, 68,
81, 67, 70, 78, 67.

Quiz score - Relative frequency:
66 to 71 - ,
72 to 77 - ,
78 to 83 - ,
84 to 89 - .

Transcript text: Rafael is taking a self-paced math class. His scores for each of the 15 quizzes during the academic year are shown below. Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 6.) Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage. \begin{tabular}{|ccccc|} \hline \multicolumn{5}{|c|}{ Quiz score } \\ \hline 89 & 85 & 72 & 66 & 76 \\ 68 & 80 & 83 & 71 & 68 \\ 81 & 67 & 70 & 78 & 67 \\ \hline \end{tabular} \begin{tabular}{|cc|} \hline Quiz score & \begin{tabular}{c} Relative \\ frequency \end{tabular} \\ \hline 66 to 71 & $\square$ \\ 72 to 77 & $\square$ \\ 78 to 83 & $\square$ \\ 84 to 89 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Frequency Distribution

We calculated the frequency of quiz scores within specified class intervals. The intervals and their corresponding frequencies are as follows:

$66$ to $71$: $7$ scores
$72$ to $77$: $2$ scores
$78$ to $83$: $4$ scores
$84$ to $89$: $2$ scores

Step 2: Total Scores

The total number of quiz scores is $15$.

Step 3: Relative Frequency Calculation

The relative frequency for each class interval is calculated using the formula:

\[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Scores}} \]

The calculated relative frequencies are:

For $66$ to $71$: \[ \text{Relative Frequency} = \frac{7}{15} \approx 0.47 \]
For $72$ to $77$: \[ \text{Relative Frequency} = \frac{2}{15} \approx 0.13 \]
For $78$ to $83$: \[ \text{Relative Frequency} = \frac{4}{15} \approx 0.27 \]
For $84$ to $89$: \[ \text{Relative Frequency} = \frac{2}{15} \approx 0.13 \]

Final Answer

The complete grouped relative frequency distribution is as follows:

Quiz score $66$ to $71$: $0.47$
Quiz score $72$ to $77$: $0.13$
Quiz score $78$ to $83$: $0.27$
Quiz score $84$ to $89$: $0.13$

Thus, the final answer is:

\[ \boxed{ \begin{array}{|cc|} \hline \text{Quiz score} & \text{Relative frequency} \\ \hline 66 \text{ to } 71 & 0.47 \\ 72 \text{ to } 77 & 0.13 \\ 78 \text{ to } 83 & 0.27 \\ 84 \text{ to } 89 & 0.13 \\ \hline \end{array} } \]

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