(Box and Whisker Plot Problem) Why is the answer choice 3 instead of choice 2?

Question

(Look at the link below) Problem #$6$ has me confused. The answer key of the textbook I am using states that the answer is choice $3$. But shouldn't the answer be choice $2$ ( $7$ students ) because the numbers, $81$ through $88$, are below Q$3$?

Answer 1

Yes, you are correct. The plot shows that the median ($2$nd quartile) is $81$, and that the $3$rd quartile is at $88$, so this range should contain exactly $28(0.25)=7$ students.

Answer 2

The question cannot be answered from the given box plot.

Example:

Any ordered score set for $28$ students of the following type would produce the same box plot:

(I have difficulty to read the $Q_3$ from your picture, so I assume it to be $Q_3= 88$.) $$\begin{pmatrix} Place: & 1 & \cdots & 7 & 8 & \cdots & 14 & 15 & \cdots & 21 & 22 & \cdots & 28 \\ Score: & 62 & \cdots & 71 & 71 & \cdots & 81 & 81 & \cdots & 88 & 88 & \cdots & 92 \end{pmatrix}$$

This would give possible numbers of scores from 81 to 88 ranging from 9 to 19.

If we assume that $Q_3 = \frac{x_{21}+x_{22}}{2}$, then consider the follwoing score set: $$\begin{pmatrix} Place: & 1 & \cdots & 7 & 8 & \cdots & 14 & 15 & \cdots & 21 & 22 & \cdots & 28 \\ Score: & 62 & \cdots & 71 & 71 & \cdots & 80 & 82 & \cdots & 87 & 89 & \cdots & 92 \end{pmatrix}$$ This would give the answer of 7 scores ranging from 81 to 88.