Students in three levels of art classes participated in the regional art competition. The two-way table below shows the number of pieces entered that were created using different media along with the level of the students who submitted the piece.

Question

Paint Clay Pastels Digital Total
Art 1 43 22 26 12 103
Art 2 34 37 14 24 109
Art 3 22 20 18 28 88
Total 99 79 58 64 300

Order the relative frequencies from least to greatest.

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

Answer 1

To determine the relative frequencies from least to greatest, we need to calculate the relevant percentages for each of the categories mentioned.

1. Percentage of clay pieces entered by Art 3 students:

   • Number of clay pieces by Art 3 students: 20
   • Total number of pieces by Art 3 students: 88
   • Percentage = (Number of clay pieces / Total pieces) × 100 \[ \text{Percentage} = \left(\frac{20}{88}\right) \times 100 \approx 22.73% \]

2. Percentage of Art 2 students who entered digital pieces:

   • Number of digital pieces by Art 2 students: 24
   • Total number of pieces by Art 2 students: 109
   • Percentage = (Number of digital pieces / Total pieces) × 100 \[ \text{Percentage} = \left(\frac{24}{109}\right) \times 100 \approx 22.01% \]

3. Percentage of all entries that were painted by Art 1 students:

   • Number of painted pieces by Art 1 students: 43
   • Total entries: 300
   • Percentage = (Number of painted pieces / Total entries) × 100 \[ \text{Percentage} = \left(\frac{43}{300}\right) \times 100 \approx 14.33% \]

Now we have the percentages:

• Clay pieces entered by Art 3 students: 22.73%
• Art 2 students who entered digital pieces: 22.01%
• All entries that were painted by Art 1 students: 14.33%

Ordering these percentages from least to greatest:

• 14.33% (Art 1 painted pieces)
• 22.01% (Art 2 digital pieces)
• 22.73% (Art 3 clay pieces)

So, the final ordered list is:

1. Percentage of all entries that were painted by Art 1 students: 14.33%
2. Percentage of Art 2 students who entered digital pieces: 22.01%
3. Percentage of clay pieces entered by Art 3 students: 22.73%