Question

the accompanying data represent the wait time (in minutes) for a random sample of forty visitors to an amusement park ride. complete parts (a) and (b)
5 1 19 12 7 5 12 25 0 7
36 24 11 6 22 56 5 8 6 8
17 19 6 77 19 32 11 21 23 16
1 6 7 24 3 18 60 7 16 17
(a) determine and interpret the quartiles.
by the quartiles, about 25% of the wait times are $q_{1}=6.0$ minute(s) or less, and about 75% of the wait times exceed $q_{1}$ minute(s); about 50% of the wait times are $q_{2}=12.0$ minute(s) or less and about 50% of the wait times exceed $q_{2}$ minute(s); about 75% of the wait times are $q_{3}=\square$ minute(s) or less, and about 25% of the wait times exceed $q_{3}$ minute(s)
(type integers or decimals. do not round.)

Explanation:

Step1: Sort the data

First, sort the given data in ascending order:
\(0,1,1,3,5,5,5,6,6,6,7,7,7,8,8,11,11,12,12,16,16,17,17,19,19,19,21,22,23,24,24,25,32,36,56,60,77\)

Step2: Find the position of \(Q_3\)

The formula for the position of the \(k\) - th quartile is \(i=\frac{k}{100}n\), where \(n = 40\) (the number of data points) and \(k = 75\) for \(Q_3\).
\(i=\frac{75}{100}\times40=30\)

Step3: Calculate \(Q_3\)

Since \(i = 30\) is an integer, \(Q_3=\frac{x_{30}+x_{31}}{2}\) (where \(x_j\) is the \(j\) - th ordered data point).
\(x_{30}=24\) and \(x_{31}=24\), so \(Q_3=\frac{24 + 24}{2}=24\)

Answer:

\(24\)