The following diagram represents the stem-and-leaf scores of sixteen students who took a Mathematics test.

1. Identify the two middle values for 16 ordered data values.

There are $16$ marks, so the median is the average of the $8$th and $9$th values.

From the ordered stem-and-leaf diagram:

$21, 54, 55, 56, 56, 57, 58, 59, 6k, 69, 71, 73, 75, 76, 79, 80$

The $8$th value is $59$ and the $9$th value is $6k$.

2. Use the given median to find $k$.

Given median $=62$,

$\frac{59+6k}{2}=62$

$59+6k=124$

$6k=65$

Since $6k$ means the two-digit mark $60+k$,

$60+k=65$

$k=5$

1. Explain why the mean is not suitable for this data set.

From the stem-and-leaf diagram, most scores are between $54$ and $80$, but there is a very low score of $21$. This extreme value would affect the mean significantly, making it not representative of the students' typical performance.