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:
211+1
=212
=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.