This data set represents the number of cups of coffee sold in a café between 8 a. m. and 10 a. m. every day for 14 days.
{10, 9, 6, 12, 4, 6, 7, 8, 15, 14, 12, 9, 10, 5}.
the difference of the values of the first and third quartiles of the data set is

To find the quartiles of the data we first arrange the data in either ascending or descending order.
{4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15}

The first quatile is the (n + 1)/4'th data = (14 + 1)/4 = 15/4 = 3.75
Therefore, the first quatile is the average of the 3rd and 4th data which is 6.

The third quartile is the 3(n + 1)/4th data = 3(15)/4 = 3(3.75) = 11.25
Therefore, the third quartile is the average of the 11th and the 12th data which is 12

Therefore, difference of the the first and the third quatile is 12 - 6 = 6.