Students in three levels of art classes participated in the regional art competition. The table below shows the number of pieces entered, categorized by media and student level:

\begin{tabular}{|l|c|c|c|c|c|}
\hline & Paint & Clay & Pastels & Digital & Total \\
\hline Art 1 & 43 & 22 & 26 & 12 & 103 \\
\hline Art 2 & 34 & 37 & 14 & 24 & 109 \\
\hline Art 3 & 22 & 20 & 18 & 28 & 88 \\
\hline Total & 99 & 79 & 58 & 64 & 300 \\
\hline
\end{tabular}

Order the relative frequencies from least to greatest:

- The percentage of all entries that were painted by Art 1 students
- The percentage of clay pieces entered by Art 3 students
- The percentage of Art 2 students who entered digital pieces



Answer :

To solve the problem of finding and ordering the relative frequencies from least to greatest for the given data, let's break it down step-by-step:

### Given Data:
1. Two-way table showing the number of pieces entered using different media along with the level of the students:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline & Paint & Clay & Pastels & Digital & Total \\ \hline Art 1 & 43 & 22 & 26 & 12 & 103 \\ \hline Art 2 & 34 & 37 & 14 & 24 & 109 \\ \hline Art 3 & 22 & 20 & 18 & 28 & 88 \\ \hline Total & 99 & 79 & 58 & 64 & 300 \\ \hline \end{tabular} \][/tex]

2. Total entries: [tex]\( 300 \)[/tex]

### Calculations for Relative Frequencies:

1. Percentage of all entries that were painted by Art 1 students:
- Number of painted pieces by Art 1 students: [tex]\( 43 \)[/tex]
- Total entries: [tex]\( 300 \)[/tex]
- Calculation: [tex]\[ \text{Percentage} = \left(\frac{43}{300}\right) \times 100 \][/tex]

[tex]\[ \text{Percentage} = 14.333333333333334\% \][/tex]


2. Percentage of clay pieces entered by Art 3 students:
- Number of clay pieces by Art 3 students: [tex]\( 20 \)[/tex]
- Total entries: [tex]\( 300 \)[/tex]
- Calculation: [tex]\[ \text{Percentage} = \left(\frac{20}{300}\right) \times 100 \][/tex]

[tex]\[ \text{Percentage} = 6.666666666666667\% \][/tex]

3. Percentage of Art 2 students who entered digital pieces:
- Number of digital pieces by Art 2 students: [tex]\( 24 \)[/tex]
- Total entries by Art 2 students: [tex]\( 109 \)[/tex]
- Calculation: [tex]\[ \text{Percentage} = \left(\frac{24}{109}\right) \times 100 \][/tex]

[tex]\[ \text{Percentage} = 22.018348623853214\% \][/tex]

### Ordering the Relative Frequencies:
1. Calculations:
- Percentage of all entries that were painted by Art 1 students: [tex]\( 14.333333333333334\% \)[/tex]
- Percentage of clay pieces entered by Art 3 students: [tex]\( 6.666666666666667\% \)[/tex]
- Percentage of Art 2 students who entered digital pieces: [tex]\( 22.018348623853214\% \)[/tex]

2. Order from least to greatest:
- [tex]\( 6.666666666666667\% \)[/tex] (Percentage of clay pieces entered by Art 3 students)
- [tex]\( 14.333333333333334\% \)[/tex] (Percentage of all entries that were painted by Art 1 students)
- [tex]\( 22.018348623853214\% \)[/tex] (Percentage of Art 2 students who entered digital pieces)

### Final Answer:
The relative frequencies ordered from least to greatest are:
[tex]\[ 6.666666666666667\%, 14.333333333333334\%, 22.018348623853214\% \][/tex]