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]
