To determine the missing value in the table, let's go through the step-by-step solution:
1. Identify the Total Number of Students:
The total number of students surveyed is given as 50.
2. Known Frequencies:
The following preferences have been recorded:
- Blue on gray: 4 students
- Green: 9 students
- Purple: 11 students
- Red and orange stripes: 9 students
3. Calculate the Remaining Students:
Add up the number of students who selected the known patterns:
[tex]\[
4 \text{ (Blue on gray)} + 9 \text{ (Green)} + 11 \text{ (Purple)} + 9 \text{ (Red and orange stripes)} = 33 \text{ students}
\][/tex]
4. Determine the Students who Chose Yellow:
Since yellow and pink polka dots are not explicitly provided, you have to account for these remaining students. Let’s find the number who selected yellow by subtracting the total of the known patterns from the total number of students:
[tex]\[
50 - 33 = 17 \text{ students}
\][/tex]
This calculation shows that 17 students selected yellow.
5. Calculate Students Choosing Pink Polka Dots:
From the overview, we know that the total missing category (which is just Pink polka dots alone) includes all remaining students after accounting for yellow:
[tex]\[
17 - 17 = 0
\][/tex]
Finally, this indicates that none of the students (0 students) selected pink polka dots.
6. Completion:
Therefore, the missing value for the Pink polka dots in the table is:
[tex]\[
\boxed{0}
\][/tex]
