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. 112
E. 122.5

Answer 1

(D) 112

Explanation:

First step: Arrange all the numbers from in ascending order that is from smallest to largest.

In Ascending order the set becomes:

45,99,108,116,118,118,118,119,120,121,124,130,148.

Second step: Find the median of the set of numbers.

Median is the middle number.

The median is 118. The median is also called the second quartile(Q2).

Third step: Now we consider all the numbers to the Left of the median(Q2). The numbers are listed below:

45,99,108,116,118,118.

Now we will find the median of these numbers.

The total numbers are 6 which is an even number.

To find the median of an even number, we add the two middle numbers and divide them by 2.

The two middle numbers are 108 and 116.

Therefore 108+116 = 224.

224/2 =112.

Therefore 112 becomes the first quartile (Q1).