The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stop watch to record the time they spent in line. The times recorded were as follows (in minutes)
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118

-What is the first quartile?
A)100.8
B)119.8
C)128.8
D)116
E)122.5

Question

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stop watch to record the time they spent in line. The times recorded were as follows (in minutes)
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118

-What is the first quartile?
A)100.8
B)119.8
C)128.8
D)116
E)122.5

Quizplus · Accepted Answer

The first quartile is the value of the observation which is greater than 25% of the other observations. To find the first quartile, we first arrange the given data in increasing order:

101, 103, 110, 112, 116, 119, 125, 130, 132, 140

The median (middle value) of the data set is the value that separates the data into two halves; that is, 116 is the median. To find the first quartile, we need to take the median of the lower half of the data set (excluding the median).

Lower half of data set: 101, 103, 110, 112

Median of lower half: (110 + 112) / 2 = 111

Therefore, the first quartile is 111, or choice D.

The Local Amusement Park Was Interested in the Average Wait