The median of the observations 1, 13, 7, 19, 18, 15, 32, 28, 23, 24, 31 is:

Given observations: 1, 13, 7, 19, 18, 15, 32, 28, 23, 24, 31

Counting the total number of observations: 11 numbers

Since there are 11 observations (odd number), the median is the middle value when arranged in order.

Arranging the numbers in ascending order:

1, 7, 13, 15, 18, 19, 23, 24, 28, 31, 32

For 11 numbers, the middle position is:

$\frac{11 + 1}{2}$

$= \frac{12}{2}$

$= 6$

The median is the 6th value in the sorted list.

Counting to the 6th position in the sorted list:

1st: 1

2nd: 7

3rd: 13

4th: 15

5th: 18

6th: 19

The median is 19.