The weights (in kg) of 14 students are measured and illustrated in the dot diagram.

1. Find the smallest and largest weights and subtract to get the range.

Smallest weight $=53$ kg

Largest weight $=60$ kg

Range $=60-53=7$ kg

1. Arrange the data in order and identify the middle positions.

The weights in ascending order are

$53, 53, 53, 54, 54, 55, 55, 57, 58, 59, 59, 59, 59, 60$.

There are $14$ weights, so the median is the average of the $7$th and $8$th values.

2. Find the average of the 7th and 8th values.

The $7$th value is $55$ and the $8$th value is $57$.

Median $= \dfrac{55+57}{2}=56$.

1. Write the data in order and split it into two equal halves.

The weights in ascending order are
$53, 53, 53, 54, 54, 55, 55, 57, 58, 59, 59, 59, 59, 60.$
There are $14$ values, so the lower half is the first $7$ values and the upper half is the last $7$ values.

2. Find the quartiles and calculate the interquartile range.

Lower half: $53, 53, 53, 54, 54, 55, 55$, so
$Q_1 = 54.$
Upper half: $57, 58, 59, 59, 59, 59, 60$, so
$Q_3 = 59.$
Hence,
$\text{interquartile range} = Q_3 - Q_1 = 59 - 54 = 5.$