Edit to correct an earlier mistake...
Order the data from lowest to highest
(1 3 4 5 6) ( 7 8 8 8 10 )
The median is [ 6 + 7] / 2 = 13/2 = 6.5
The median of the data group in the left set of parentheses is 4 = 1st quartile
The median of the data group in the second set of parentheses is 8 = 3rd quartile
The interquartile range is 8 - 4 = 4