Question

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

Answer 1

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.